Impact of Data Characteristics on Recommender Systems Performance

Size: px
Start display at page:

Download "Impact of Data Characteristics on Recommender Systems Performance"

Transcription

1 Impact of Data Characteristics on Recommender Systems Performance Gediminas Adomavicius YoungOk Kwon Jingjing Zhang Department of Information and Decision Sciences Carlson School of Management, University of Minnesota {gedas, kwonx052, Abstract. This paper investigates the impact of rating data characteristics on the performance of recommendation algorithms. We focus on three groups of data characteristics: rating density, rating frequency distribution, and rating value distribution. We introduce a window sampling procedure that can effectively manipulate the characteristics of rating samples and apply regression model to uncover the relationships between data characteristics and recommendation accuracy. Our experimental results show that the recommendation accuracy is highly influenced by structural characteristics of rating data, and the effects of data characteristics are consistent for different recommendation techniques. Understanding how data characteristics can impact the recommendation performance has practical significance and can enable the recommender system designers to estimate the expected performance of their system in advance and, thus, to direct data collection efforts to maximize the recommendation performance. 1. Introduction and Motivation Recommender systems analyze patterns of user preferences and attempt to recommend items that are likely to interest users. In many applications, recommender systems use the notion of ratings to model user preferences for items, and the ratings in these systems can be used as inputs (i.e., known ratings for items that users provided in the past) as well as outputs (i.e., rating predictions for items that have not been consumed by users). A lot of research in recommender systems literature has been focusing on improving the recommendation performance (usually measured by the accuracy of rating predictions), typically by proposing novel and increasingly more sophisticated recommendation algorithms. It is well recognized that rating data can often be highly sparse and skewed and that this can have a significant impact on recommender systems performance [1,7]; however, little research has been dedicated to providing a systematic, in-depth exploration and analysis of this issue. Understanding this has great practical significance as well. For example, this would enable the recommender system designers to estimate the expected performance of their system in advance (i.e., based on simple data characteristics) and, thus, to direct data collection efforts to maximize the performance of a recommendation algorithm. This study uses regression-based explanatory modeling techniques to investigate which rating data characteristics can be associated with the variations in recommendation performance of several popular recommendation algorithms. In this paper, we focus on three categories of rating data characteristics: rating density, rating distribution, and rating values, as described below. 2. Measures for Rating Data: Proposed Approach and Related Work Overall Rating Density. Data sparsity is a problem that is common to most recommender systems due to the fact that users typically rate only a small proportion of the available items [1]. This can be aggravated by the fact that users or items newly added to the system may have no ratings at all, known as a cold-start problem. If the rating data is sparse, two users are unlikely to have many items in common, thus, causing some algorithms (e.g., neighborhood-based CF techniques) to have poor performance in terms of recommendation accuracy, and there have been several studies dedicated to alleviating the sparsity problem [2,3,9]. In this paper, we use a traditional approach to measuring the overall rating density, i.e., by calculating the proportion of known ratings (i.e., provided by the users to the system) among all possible ratings that can possibly be given by the users. The operating assumption is that sparser rating data would lead to lower accuracy, and we will explore this relationship with different density configurations. Rating Frequency Distribution. Recommender systems data (e.g., in retail shopping applications) is typically not only sparse but also skewed, often exhibiting long-tail distribution,

2 where few ( popular ) items are bought very frequently, but most items are bought only very few times. In other words, popularity of an item is typically represented by the number of users who bought/rated it. For example, up to 80 percent of all Netflix movie rentals are long-tail movies [4] and Netflix is making more money with the long tail (i.e., the back-catalog titles and indie movies that cannot be easily found at a local Blockbuster or Best Buy) than with current releases [12]. However, long-tail items often have limited historical data and, if included in recommendation models, can possibly lead to a decrease in the performance of recommender systems. We explored several measures for characterizing the structural distribution of rating data, including the basic shape of frequency distribution of user or item ratings (using the first four moments: mean, variance, skewness, kurtosis) as well as the concentration of items or users in the frequency distribution (using standard measures, such as Gini coefficient and Herfindahl index). Many of these metrics were highly correlated for the rating datasets that we had; after preliminary analysis (e.g., elimination of redundant/correlated metrics), skewness and Gini coefficient were chosen as best representative metrics for different aspects of rating distribution. In particular, skewness (also called the third central moment in mathematical statistics) measures the asymmetry of an item (or user) frequency (popularity) distribution, and is defined as: 3 3/ 2 X 1 n 3 1 n 2 Skewness = E μ = ( x ) ( ) i= 1 i μ x i= 1 i μ, σ n n where μ is the mean and σ is the standard deviation of item popularity, and x i represents the popularity of item i, as defined by the number of users who rated it. This metric determines whether the mass of the distribution is concentrated on the right side of the mean or the left side of the mean, i.e., representing negative or positive skewness as shown in Fig. 1a. In contrast, Gini coefficient measures the concentration (or inequality) of an item (or user) frequency distribution [6]. It is a commonly used metric of wealth distribution inequality in economics and can be computed as the ratio of the area between the line of equality and the Lorenz curve (shown in Fig. 1b) that represents cumulative frequency of users or items arranged in the ascending order based on their popularity (i.e., area A), over the total area under the line of equality (i.e., area A+B). Formally, for discrete distributions it can be defined as follows: n n + 1 i xi Gini = A ( A + B) = 1 B ( A + B) = 1 2 =, i 1 n + 1 total where x i is the popularity of item i, n is the total number of items available in the dataset, and total is the total number of ratings. Thus, a value of 0 represents total equality (all items are equally popular), and a value of 1 represents maximal inequality (a few popular items have all the ratings). These two metrics quantify two different properties of an item (or user) frequency distribution. For example, our experiments show that skewness is sensitive to the number of items that are below/above the average item popularity, but Gini coefficient is sensitive to the actual item popularity numbers (e.g., the frequency of the most popular vs. least popular item). Fig. 1c shows an example of two distributions with the same exact Gini coefficient (0.23), where one distribution has a positive (1.72) and the other negative (-0.75) skewness. Rating Value. After exploring several basic statistics of rating value distribution, we found the rating variance to be the most informative rating-value-related measure when analyzing the impact of data characteristics on recommender systems performance. Rating variance has been explored in recommender systems literature before. For example, uncertainty of an item s rating is often measured by its variance, and a highly controversial item tends to have higher rating variance in the user population. High variance data is not necessarily considered bad data, but can be the

3 cause of recommendation errors [7]. There has also been some positive evidence for high rating variance. For example, when faced with two movies with pre-calculated ratings, consumers have been found to prefer the high variance movie [11]; also, in some settings high rating variance can positively affect consumers purchase decisions and increase subsequent demand and profit [13]. (a) Skewness (b) Gini coefficient (c) Example: different skewness with the same Gini coefficient Figure 1. Rating distribution metrics: skewness and Gini coefficient Analyzing Impact of Data Characteristics on Recommendation Performance. While prior literature provides some discussion on how individual data characteristics may affect recommendation performance, in this paper we propose a more systematic way to explore the underlying relationship between a set of representative data characteristics and recommendation accuracy. This analysis provides new insights and understanding about which data characteristics play a more important (or less important) role and, as a result, can help system designers in improving the performance of recommender systems. Using the aforementioned metrics (i.e., rating density, movie skewness, user skewness, movie Gini, user Gini, and rating variance) that, we believe, can play an important role in explaining variations in recommendation accuracy, we build the following explanatory model, the analysis of which will be discussed in the next section: Recommendation Accuracy = β 0 + β 1 *Density + β 2 *movieskewness + β 3 *userskewness + β 4 *moviegini + β 5 *usergini + β 6 *. 3. Experimental Results Dataset and Sampling Procedure. We used the publicly available MovieLens 1M movie rating dataset (available at movielens.org) to examine the relationship between data characteristics and accuracy of popular recommendation algorithms. This dataset consists of 1 million ratings for 6040 movies by 3952 users (i.e., data density is 4.2%). All ratings are integers between 1 and 5. In order to create datasets with different data characteristics, we propose to use the window sampling procedure for extracting a variety of samples from the original dataset. For data preparation, ratings are read into a rating matrix, each column representing an item and each row representing a user. Rows and columns of the rating matrix are then rearranged according to the frequency distribution, i.e., the first column represents the most rated movie and the first row represents the user who provided the most ratings, and so on. As illustrated by Fig. 2a and 2b, after rearranging rows and columns, the new rating matrix becomes more extremely distributed than original matrix, i.e., data is highly dense in one corner but highly sparse in the opposite one. A rectangle-shaped window of a fixed size is then moved around the sorted rating matrix, and ratings that fit within the boundaries of the window are extracted as a sample. Fig. 2c visualizes the window and some of the samples obtained from sorted rating matrix based on Movielens 1M dataset. In our experiments, size of the rectangle window was set to 300 users 200 items. The step size each time the window moves was set to be proportional to the rating density, so that the

4 window moves slower when data is dense and faster when data is sparse. The reason for adjusting movement speed is because the majority of the original matrix is very sparse and, hence, we need to extract enough samples from the denser area to ensure the richness of sample representation. In addition, to ensure that each sample has a sufficient amount of data for recommendation algorithms to make meaningful predictions, only samples that have rating density above 6% are considered in our experiments. We used this specific threshold to ensure that the recommendation algorithm versions tested in our experiments all have sufficient prediction coverage. (Experiments with lower thresholds produced comparable results in the follow-up study.) In total, we extracted 1384 samples exhibiting varying characteristics in terms of rating density, distribution, and value. Sample 1 Sample 2 Sample 3 Sample n (a) Original Matrix (b) Rearranged Matrix (c) Window Sampling Figure 2. (a) Original Rating Matrix, (b) Rearranged Matrix, and (c) Window Sampling Illustration Recommendation Algorithms. In this paper we focus on two of the most widely used collaborative filtering (CF) techniques for recommender systems neighborhood-based and matrix factorization CF approaches to test the general validity of the proposed premise. A neighborhood-based CF approach predicts unknown ratings of a user based on the ratings of the nearest neighbor users who have similar rating patterns [2]. This technique can be user-based (as described above) or item-based, if the ratings of the nearest neighbor items are used to predict unknown ratings of an item [3]. Matrix factorization technique estimates each unknown rating as an inner product of user- and item-factors vectors that indicate the preference of a user for several latent features and an item s importance weights for the same number of features, respectively [5,10]. Many variations of matrix factorization techniques have been developed in the Netflix Prize competition and have proven to be effective in terms of recommendation accuracy. The basic version of the matrix factorization technique [5] as well as both user- and item-based neighborhood CF approaches were used in our experiments. Also, our experiments follow the standard process of 5-fold cross validation and test the impact of dataset characteristics on prediction accuracy of three recommendation techniques mentioned above. Recommendation accuracy was measured by the standard measure of root mean squared error (RMSE) [8]. Regression Analysis. As discussed earlier, in our study we chose to use 6 independent variables (IVs): rating density, gini coefficients and skewness indices for user and item rating frequency distributions, and rating variance. The dependent variable is the prediction error of each of the three popular recommendation algorithms as measured by RMSE. A linear regression model was built to explain the relation between six IVs and DV for each algorithm. All IVs were centered by subtracting their mean. This zero-mean centering transformation does not affect the relationship between variables, but it makes the regression models easier to interpret. A thorough examination of correlation of IVs did not raise collinearity issues. Regression results of the three recommendation techniques are summarized in Table 1. Results of data analysis show that the six data characteristics can explain 80.1, 75.7, and 79.7% of the

5 variance in recommendation RMSE made by item-based CF, user-based CF, and matrix factorization techniques, respectively. Hence, we can draw the conclusion that data characteristics play a significant role in determining the accuracy of recommendation algorithms. Table 1. Summary of Regression Results Item-based CF User-based CF Matrix Factorization R 2 (Adjusted R 2 ).801 (.800).757 (.756).797 (.797) coefficient T coefficient T coefficient t Constant **** **** **** Density **** **** **** **** **** **** moviegini **** * usergini **** **** **** movieskewness **** **** **** userskewness **** **** **** **** p , *** p 0.001, ** p 0.01, * p 0.05 Since IVs are centered to have zero mean values, the constant component in a regression model represents the expected recommendation accuracy (measured in RMSE) of a given technique on a dataset with average rating density, variance, and frequency distribution. Results suggest that, for a dataset with average characteristics, matrix factorization has the smallest expected RMSE (i.e., 0.940), followed by item-based CF (i.e., 0.956), and user-based CF has the largest expected RMSE (i.e., 0.967). This confirms the findings in recommender system literature that matrix factorization technique typically gives better accuracy than neighborhood-based collaborative filtering approaches [10], and item-based techniques often outperform user-based ones [3]. Overall, the relationships between six IVs and RMSE are found to be significant. Signs of regression coefficients for three models are consistent. For example, rating density has negative effects on RMSE for all three techniques (i.e., , and , respectively), i.e., denser dataset leads to better accuracy. Comparing regression coefficients of density, it seems that matrix factorization is less sensitive to data density than neighborhood-based CF approaches. As another example, rating variance has positive impacts on RMSE (0.158, and 0.135), meaning that dataset with smaller variations in rating values tends to provide better accuracy. Table 2. Sequence of Variables in Stepwise Regression Model Movie-based CF User-based CF Matrix Factorization Predictors R 2 Predictors R 2 Predictors R 2 1 Density.696 Density.625 Density Density.768 Density.730 Density.755 Final Density userskewness usergini movieskewness moviegini.801 Density userskewness movieskewness usergini.757 Density userskewness movieskewness usergini moviegini We also examine the level of importance of six IVs using stepwise regression. Sequence of variables added to the regression model is a proxy for the rank of contribution of the variables in explaining variations in RMSE. Stepwise regression results are provided in Table 2. For all three algorithms, dataset density is found to be the most important variable in the analysis. Including density alone in the model is able to explain 69.6, 62.5, and 56.7% of the variance in RMSE for item-based CF, user-based CF, and matrix factorization, respectively. Further, the next most.797

6 important variable is the rating variance. Together with density, the two variables can explain 76.8, 73.0, and 75.5% of the variations in RMSE for the three techniques. Frequency distribution statistics (i.e., Gini and skewness) are added to the models last, in slightly different orders. These four distributional metrics are able to provide further improvements to R 2. To check the robustness of our results, we ran a second set of experiments with Netflix Prize dataset. The findings (not presented here due to the space limitations) were consistent with results reported above. 6. Discussion and Conclusion The objective of this study is to investigate the relationship between dataset characteristics and accuracy of popular collaborative filtering techniques. To prepare datasets with varying characteristics, we introduce the window sampling procedure to extract samples characterized with different rating densities, rating frequency distributions, and rating value distributions. Our experiment results show that recommendation accuracy is highly influenced by structural characteristics of the dataset, and the effects of these characteristics are consistent across different recommendation techniques. Using six simple variables, one can explain about 80% of the variation in RMSE. Moreover, our results also show that, among the six characteristics, rating density is the most important variable in explaining variation of the recommendation accuracy, followed by rating variance, and then descriptive statistics for rating frequency distribution. In terms of practical implications, by analyzing customers usage and preference patterns and understanding the evolution of rating dataset characteristics, firms would be able to anticipate the performance changes of their systems. Further, this allows firms to strategically direct their efforts (e.g., by designing user interfaces that promote certain types of user-system interactions) toward more favorable data distributions in order to maximize performance of their recommender systems. We believe that the impact of dataset characteristics on accuracy of recommendation algorithms deserves our attention and exploration in both research and practice, and that significant additional work is needed to explore this issue in a more comprehensive manner. Acknowledgement This research was supported in part by the National Science Foundation grant IIS References [1] G. Adomavicius and A. Tuzhilin, Toward the next generation of recommender systems: A survey of the state-ofthe-art and possible extensions, IEEE Trans. on Knowledge and Data Eng., 17(6): , [2] J.S. Breese, D. Heckerman, C. Kadie, Empirical analysis of predictive algorithms for collaborative filtering, In Proc. of the 14th Annual Conf. on Uncertainty in Artificial intelligence, pp , [3] M. Deshpande, G. Karypis, Item-based top-n recommendation algorithms, ACM Transactions on Information Systems, 22(1), pp , [4] L.J. Flynn, Like This? You'll Hate That. New York Times, Jan [5] S. Funk, Netflix Update: Try This at Home, Available at: [6] C. Gini, Measurement of Inequality and Incomes, The Economic Journal, 31, pp , [7] J. L. Herlocker, J.A. Konstan, and J. Riedl, Explaining Collaborative Filtering Recommendations, In Proc. of the 2000 ACM conference on Computer supported cooperative work, pp , [8] J.L. Herlocker, J.A. Konstan, L.G. Terveen, and J. Riedl, Evaluating collaborative filtering recommender systems, ACM Transaction on Information Systems, 22(1), pp. 5 53, [9] Z. Huang, H.Chen, D. Zeng, Applying associative retrieval techniques to alleviate the sparsity problem in collaborative filtering, ACM Transactions on Information Systems, 22(1), pp , [10] Y. Koren, R. Bell, and C. Volinsky, Matrix Factorization Techniques For Recommender Systems, IEEE Computer Society, 42, pp , [11] J. Martin, G. Barron, and M.I. Norton, Choosing to Be Uncertain: Preferences for High Variance Experiences. Working Paper, Harvard Business School, [12] J. Roettgers, Warner Bros.-Netflix Deal is All About the Long Tail, Jan [13] M. Sun, How Does Variance of Product Ratings Matter?, abstract= , 2010.

Collaborative Filtering. Radek Pelánek

Collaborative Filtering. Radek Pelánek Collaborative Filtering Radek Pelánek 2017 Notes on Lecture the most technical lecture of the course includes some scary looking math, but typically with intuitive interpretation use of standard machine

More information

Collaborative Filtering on Ordinal User Feedback

Collaborative Filtering on Ordinal User Feedback Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Collaborative Filtering on Ordinal User Feedback Yehuda Koren Google yehudako@gmail.com Joseph Sill Analytics Consultant

More information

Predicting the Performance of Collaborative Filtering Algorithms

Predicting the Performance of Collaborative Filtering Algorithms Predicting the Performance of Collaborative Filtering Algorithms Pawel Matuszyk and Myra Spiliopoulou Knowledge Management and Discovery Otto-von-Guericke University Magdeburg, Germany 04. June 2014 Pawel

More information

Collaborative topic models: motivations cont

Collaborative topic models: motivations cont Collaborative topic models: motivations cont Two topics: machine learning social network analysis Two people: " boy Two articles: article A! girl article B Preferences: The boy likes A and B --- no problem.

More information

Matrix Factorization Techniques For Recommender Systems. Collaborative Filtering

Matrix Factorization Techniques For Recommender Systems. Collaborative Filtering Matrix Factorization Techniques For Recommender Systems Collaborative Filtering Markus Freitag, Jan-Felix Schwarz 28 April 2011 Agenda 2 1. Paper Backgrounds 2. Latent Factor Models 3. Overfitting & Regularization

More information

* Matrix Factorization and Recommendation Systems

* Matrix Factorization and Recommendation Systems Matrix Factorization and Recommendation Systems Originally presented at HLF Workshop on Matrix Factorization with Loren Anderson (University of Minnesota Twin Cities) on 25 th September, 2017 15 th March,

More information

Collaborative Filtering via Ensembles of Matrix Factorizations

Collaborative Filtering via Ensembles of Matrix Factorizations Collaborative Ftering via Ensembles of Matrix Factorizations Mingrui Wu Max Planck Institute for Biological Cybernetics Spemannstrasse 38, 72076 Tübingen, Germany mingrui.wu@tuebingen.mpg.de ABSTRACT We

More information

Recommender Systems. Dipanjan Das Language Technologies Institute Carnegie Mellon University. 20 November, 2007

Recommender Systems. Dipanjan Das Language Technologies Institute Carnegie Mellon University. 20 November, 2007 Recommender Systems Dipanjan Das Language Technologies Institute Carnegie Mellon University 20 November, 2007 Today s Outline What are Recommender Systems? Two approaches Content Based Methods Collaborative

More information

Binary Principal Component Analysis in the Netflix Collaborative Filtering Task

Binary Principal Component Analysis in the Netflix Collaborative Filtering Task Binary Principal Component Analysis in the Netflix Collaborative Filtering Task László Kozma, Alexander Ilin, Tapani Raiko first.last@tkk.fi Helsinki University of Technology Adaptive Informatics Research

More information

Modeling User Rating Profiles For Collaborative Filtering

Modeling User Rating Profiles For Collaborative Filtering Modeling User Rating Profiles For Collaborative Filtering Benjamin Marlin Department of Computer Science University of Toronto Toronto, ON, M5S 3H5, CANADA marlin@cs.toronto.edu Abstract In this paper

More information

Preliminaries. Data Mining. The art of extracting knowledge from large bodies of structured data. Let s put it to use!

Preliminaries. Data Mining. The art of extracting knowledge from large bodies of structured data. Let s put it to use! Data Mining The art of extracting knowledge from large bodies of structured data. Let s put it to use! 1 Recommendations 2 Basic Recommendations with Collaborative Filtering Making Recommendations 4 The

More information

Matrix Factorization Techniques for Recommender Systems

Matrix Factorization Techniques for Recommender Systems Matrix Factorization Techniques for Recommender Systems By Yehuda Koren Robert Bell Chris Volinsky Presented by Peng Xu Supervised by Prof. Michel Desmarais 1 Contents 1. Introduction 4. A Basic Matrix

More information

Probabilistic Partial User Model Similarity for Collaborative Filtering

Probabilistic Partial User Model Similarity for Collaborative Filtering Probabilistic Partial User Model Similarity for Collaborative Filtering Amancio Bouza, Gerald Reif, Abraham Bernstein Department of Informatics, University of Zurich {bouza,reif,bernstein}@ifi.uzh.ch Abstract.

More information

A Modified PMF Model Incorporating Implicit Item Associations

A Modified PMF Model Incorporating Implicit Item Associations A Modified PMF Model Incorporating Implicit Item Associations Qiang Liu Institute of Artificial Intelligence College of Computer Science Zhejiang University Hangzhou 31007, China Email: 01dtd@gmail.com

More information

Probabilistic Neighborhood Selection in Collaborative Filtering Systems

Probabilistic Neighborhood Selection in Collaborative Filtering Systems Probabilistic Neighborhood Selection in Collaborative Filtering Systems Panagiotis Adamopoulos and Alexander Tuzhilin Department of Information, Operations and Management Sciences Leonard N. Stern School

More information

Collaborative Filtering Using Orthogonal Nonnegative Matrix Tri-factorization

Collaborative Filtering Using Orthogonal Nonnegative Matrix Tri-factorization Collaborative Filtering Using Orthogonal Nonnegative Matrix Tri-factorization Gang Chen 1,FeiWang 1, Changshui Zhang 2 State Key Laboratory of Intelligent Technologies and Systems Tsinghua University 1

More information

CS 175: Project in Artificial Intelligence. Slides 4: Collaborative Filtering

CS 175: Project in Artificial Intelligence. Slides 4: Collaborative Filtering CS 175: Project in Artificial Intelligence Slides 4: Collaborative Filtering 1 Topic 6: Collaborative Filtering Some slides taken from Prof. Smyth (with slight modifications) 2 Outline General aspects

More information

Collaborative Filtering with Aspect-based Opinion Mining: A Tensor Factorization Approach

Collaborative Filtering with Aspect-based Opinion Mining: A Tensor Factorization Approach 2012 IEEE 12th International Conference on Data Mining Collaborative Filtering with Aspect-based Opinion Mining: A Tensor Factorization Approach Yuanhong Wang,Yang Liu, Xiaohui Yu School of Computer Science

More information

Integrated Electricity Demand and Price Forecasting

Integrated Electricity Demand and Price Forecasting Integrated Electricity Demand and Price Forecasting Create and Evaluate Forecasting Models The many interrelated factors which influence demand for electricity cannot be directly modeled by closed-form

More information

Andriy Mnih and Ruslan Salakhutdinov

Andriy Mnih and Ruslan Salakhutdinov MATRIX FACTORIZATION METHODS FOR COLLABORATIVE FILTERING Andriy Mnih and Ruslan Salakhutdinov University of Toronto, Machine Learning Group 1 What is collaborative filtering? The goal of collaborative

More information

Algorithms for Collaborative Filtering

Algorithms for Collaborative Filtering Algorithms for Collaborative Filtering or How to Get Half Way to Winning $1million from Netflix Todd Lipcon Advisor: Prof. Philip Klein The Real-World Problem E-commerce sites would like to make personalized

More information

Matrix Factorization with Content Relationships for Media Personalization

Matrix Factorization with Content Relationships for Media Personalization Association for Information Systems AIS Electronic Library (AISeL) Wirtschaftsinformatik Proceedings 013 Wirtschaftsinformatik 013 Matrix Factorization with Content Relationships for Media Personalization

More information

Collaborative filtering based on multi-channel diffusion

Collaborative filtering based on multi-channel diffusion Collaborative filtering based on multi-channel Ming-Sheng Shang a Ci-Hang Jin b Tao Zhou b Yi-Cheng Zhang a,b arxiv:0906.1148v1 [cs.ir] 5 Jun 2009 a Lab of Information Economy and Internet Research,University

More information

DRIVING ROI. The Business Case for Advanced Weather Solutions for the Energy Market

DRIVING ROI. The Business Case for Advanced Weather Solutions for the Energy Market DRIVING ROI The Business Case for Advanced Weather Solutions for the Energy Market Table of Contents Energy Trading Challenges 3 Skill 4 Speed 5 Precision 6 Key ROI Findings 7 About The Weather Company

More information

Decoupled Collaborative Ranking

Decoupled Collaborative Ranking Decoupled Collaborative Ranking Jun Hu, Ping Li April 24, 2017 Jun Hu, Ping Li WWW2017 April 24, 2017 1 / 36 Recommender Systems Recommendation system is an information filtering technique, which provides

More information

Collaborative Filtering with Temporal Dynamics with Using Singular Value Decomposition

Collaborative Filtering with Temporal Dynamics with Using Singular Value Decomposition ISSN 1330-3651 (Print), ISSN 1848-6339 (Online) https://doi.org/10.17559/tv-20160708140839 Original scientific paper Collaborative Filtering with Temporal Dynamics with Using Singular Value Decomposition

More information

NCDREC: A Decomposability Inspired Framework for Top-N Recommendation

NCDREC: A Decomposability Inspired Framework for Top-N Recommendation NCDREC: A Decomposability Inspired Framework for Top-N Recommendation Athanasios N. Nikolakopoulos,2 John D. Garofalakis,2 Computer Engineering and Informatics Department, University of Patras, Greece

More information

Matrix Factorization In Recommender Systems. Yong Zheng, PhDc Center for Web Intelligence, DePaul University, USA March 4, 2015

Matrix Factorization In Recommender Systems. Yong Zheng, PhDc Center for Web Intelligence, DePaul University, USA March 4, 2015 Matrix Factorization In Recommender Systems Yong Zheng, PhDc Center for Web Intelligence, DePaul University, USA March 4, 2015 Table of Contents Background: Recommender Systems (RS) Evolution of Matrix

More information

Glossary. The ISI glossary of statistical terms provides definitions in a number of different languages:

Glossary. The ISI glossary of statistical terms provides definitions in a number of different languages: Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the

More information

Predicting Neighbor Goodness in Collaborative Filtering

Predicting Neighbor Goodness in Collaborative Filtering Predicting Neighbor Goodness in Collaborative Filtering Alejandro Bellogín and Pablo Castells {alejandro.bellogin, pablo.castells}@uam.es Universidad Autónoma de Madrid Escuela Politécnica Superior Introduction:

More information

A METHOD OF FINDING IMAGE SIMILAR PATCHES BASED ON GRADIENT-COVARIANCE SIMILARITY

A METHOD OF FINDING IMAGE SIMILAR PATCHES BASED ON GRADIENT-COVARIANCE SIMILARITY IJAMML 3:1 (015) 69-78 September 015 ISSN: 394-58 Available at http://scientificadvances.co.in DOI: http://dx.doi.org/10.1864/ijamml_710011547 A METHOD OF FINDING IMAGE SIMILAR PATCHES BASED ON GRADIENT-COVARIANCE

More information

Forecasting Using Time Series Models

Forecasting Using Time Series Models Forecasting Using Time Series Models Dr. J Katyayani 1, M Jahnavi 2 Pothugunta Krishna Prasad 3 1 Professor, Department of MBA, SPMVV, Tirupati, India 2 Assistant Professor, Koshys Institute of Management

More information

Large-scale Ordinal Collaborative Filtering

Large-scale Ordinal Collaborative Filtering Large-scale Ordinal Collaborative Filtering Ulrich Paquet, Blaise Thomson, and Ole Winther Microsoft Research Cambridge, University of Cambridge, Technical University of Denmark ulripa@microsoft.com,brmt2@cam.ac.uk,owi@imm.dtu.dk

More information

a Short Introduction

a Short Introduction Collaborative Filtering in Recommender Systems: a Short Introduction Norm Matloff Dept. of Computer Science University of California, Davis matloff@cs.ucdavis.edu December 3, 2016 Abstract There is a strong

More information

Recommender Systems EE448, Big Data Mining, Lecture 10. Weinan Zhang Shanghai Jiao Tong University

Recommender Systems EE448, Big Data Mining, Lecture 10. Weinan Zhang Shanghai Jiao Tong University 2018 EE448, Big Data Mining, Lecture 10 Recommender Systems Weinan Zhang Shanghai Jiao Tong University http://wnzhang.net http://wnzhang.net/teaching/ee448/index.html Content of This Course Overview of

More information

1 Bewley Economies with Aggregate Uncertainty

1 Bewley Economies with Aggregate Uncertainty 1 Bewley Economies with Aggregate Uncertainty Sofarwehaveassumedawayaggregatefluctuations (i.e., business cycles) in our description of the incomplete-markets economies with uninsurable idiosyncratic risk

More information

Recommender System for Yelp Dataset CS6220 Data Mining Northeastern University

Recommender System for Yelp Dataset CS6220 Data Mining Northeastern University Recommender System for Yelp Dataset CS6220 Data Mining Northeastern University Clara De Paolis Kaluza Fall 2016 1 Problem Statement and Motivation The goal of this work is to construct a personalized recommender

More information

Collaborative Recommendation with Multiclass Preference Context

Collaborative Recommendation with Multiclass Preference Context Collaborative Recommendation with Multiclass Preference Context Weike Pan and Zhong Ming {panweike,mingz}@szu.edu.cn College of Computer Science and Software Engineering Shenzhen University Pan and Ming

More information

6.034 Introduction to Artificial Intelligence

6.034 Introduction to Artificial Intelligence 6.34 Introduction to Artificial Intelligence Tommi Jaakkola MIT CSAIL The world is drowning in data... The world is drowning in data...... access to information is based on recommendations Recommending

More information

Recommendation Systems

Recommendation Systems Recommendation Systems Popularity Recommendation Systems Predicting user responses to options Offering news articles based on users interests Offering suggestions on what the user might like to buy/consume

More information

NetBox: A Probabilistic Method for Analyzing Market Basket Data

NetBox: A Probabilistic Method for Analyzing Market Basket Data NetBox: A Probabilistic Method for Analyzing Market Basket Data José Miguel Hernández-Lobato joint work with Zoubin Gharhamani Department of Engineering, Cambridge University October 22, 2012 J. M. Hernández-Lobato

More information

Generative Models for Discrete Data

Generative Models for Discrete Data Generative Models for Discrete Data ddebarr@uw.edu 2016-04-21 Agenda Bayesian Concept Learning Beta-Binomial Model Dirichlet-Multinomial Model Naïve Bayes Classifiers Bayesian Concept Learning Numbers

More information

A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation

A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation Yue Ning 1 Yue Shi 2 Liangjie Hong 2 Huzefa Rangwala 3 Naren Ramakrishnan 1 1 Virginia Tech 2 Yahoo Research. Yue Shi

More information

Warwick Business School Forecasting System. Summary. Ana Galvao, Anthony Garratt and James Mitchell November, 2014

Warwick Business School Forecasting System. Summary. Ana Galvao, Anthony Garratt and James Mitchell November, 2014 Warwick Business School Forecasting System Summary Ana Galvao, Anthony Garratt and James Mitchell November, 21 The main objective of the Warwick Business School Forecasting System is to provide competitive

More information

Collaborative Filtering Applied to Educational Data Mining

Collaborative Filtering Applied to Educational Data Mining Journal of Machine Learning Research (200) Submitted ; Published Collaborative Filtering Applied to Educational Data Mining Andreas Töscher commendo research 8580 Köflach, Austria andreas.toescher@commendo.at

More information

CMAP: Effective Fusion of Quality and Relevance for Multi-criteria Recommendation

CMAP: Effective Fusion of Quality and Relevance for Multi-criteria Recommendation CMAP: Effective Fusion of Quality and Relevance for Multi-criteria Recommendation ABSTRACT Xin Xin, Michael R. Lyu Dept. of Computer Science and Engineering The Chinese University of Hong Kong Shatin,

More information

Using the Budget Features in Quicken 2008

Using the Budget Features in Quicken 2008 Using the Budget Features in Quicken 2008 Quicken budgets can be used to summarize expected income and expenses for planning purposes. The budget can later be used in comparisons to actual income and expenses

More information

Recommender Systems: Overview and. Package rectools. Norm Matloff. Dept. of Computer Science. University of California at Davis.

Recommender Systems: Overview and. Package rectools. Norm Matloff. Dept. of Computer Science. University of California at Davis. Recommender December 13, 2016 What Are Recommender Systems? What Are Recommender Systems? Various forms, but here is a common one, say for data on movie ratings: What Are Recommender Systems? Various forms,

More information

Recommendation Systems

Recommendation Systems Recommendation Systems Pawan Goyal CSE, IITKGP October 21, 2014 Pawan Goyal (IIT Kharagpur) Recommendation Systems October 21, 2014 1 / 52 Recommendation System? Pawan Goyal (IIT Kharagpur) Recommendation

More information

Mining Positive and Negative Fuzzy Association Rules

Mining Positive and Negative Fuzzy Association Rules Mining Positive and Negative Fuzzy Association Rules Peng Yan 1, Guoqing Chen 1, Chris Cornelis 2, Martine De Cock 2, and Etienne Kerre 2 1 School of Economics and Management, Tsinghua University, Beijing

More information

arxiv: v2 [cs.ir] 14 May 2018

arxiv: v2 [cs.ir] 14 May 2018 A Probabilistic Model for the Cold-Start Problem in Rating Prediction using Click Data ThaiBinh Nguyen 1 and Atsuhiro Takasu 1, 1 Department of Informatics, SOKENDAI (The Graduate University for Advanced

More information

Masters of Marketing Spotlight Series

Masters of Marketing Spotlight Series Masters of Marketing Spotlight Series Dan Alexander CO-FOUNDER / CHIEF METEOROLOGIST & DATA SCIENTIST WEATHERALPHA Carl Weber DIRECTOR, BUSINESS DEVELOPMENT WEATHERALPHA Dan Alexander, co-founder and chief

More information

arxiv: v1 [cs.ir] 16 Oct 2013

arxiv: v1 [cs.ir] 16 Oct 2013 An FCA-based Boolean Matrix Factorisation for Collaborative Filtering Elena Nenova 2,1, Dmitry I. Ignatov 1, and Andrey V. Konstantinov 1 1 National Research University Higher School of Economics, Moscow

More information

CS425: Algorithms for Web Scale Data

CS425: Algorithms for Web Scale Data CS: Algorithms for Web Scale Data Most of the slides are from the Mining of Massive Datasets book. These slides have been modified for CS. The original slides can be accessed at: www.mmds.org Customer

More information

Quantifying Weather Risk Analysis

Quantifying Weather Risk Analysis Quantifying Weather Risk Analysis Now that an index has been selected and calibrated, it can be used to conduct a more thorough risk analysis. The objective of such a risk analysis is to gain a better

More information

Forecasting. Dr. Richard Jerz rjerz.com

Forecasting. Dr. Richard Jerz rjerz.com Forecasting Dr. Richard Jerz 1 1 Learning Objectives Describe why forecasts are used and list the elements of a good forecast. Outline the steps in the forecasting process. Describe at least three qualitative

More information

SCMF: Sparse Covariance Matrix Factorization for Collaborative Filtering

SCMF: Sparse Covariance Matrix Factorization for Collaborative Filtering SCMF: Sparse Covariance Matrix Factorization for Collaborative Filtering Jianping Shi Naiyan Wang Yang Xia Dit-Yan Yeung Irwin King Jiaya Jia Department of Computer Science and Engineering, The Chinese

More information

Kernelized Matrix Factorization for Collaborative Filtering

Kernelized Matrix Factorization for Collaborative Filtering Kernelized Matrix Factorization for Collaborative Filtering Xinyue Liu Charu Aggarwal Yu-Feng Li Xiangnan Kong Xinyuan Sun Saket Sathe Abstract Matrix factorization (MF) methods have shown great promise

More information

Exploring the Ratings Prediction Task in a Group Recommender System that Automatically Detects Groups

Exploring the Ratings Prediction Task in a Group Recommender System that Automatically Detects Groups Exploring the Ratings Prediction Task in a Group Recommender System that Automatically Detects Groups Ludovico Boratto and Salvatore Carta Dip.to di Matematica e Informatica Università di Cagliari Via

More information

From Non-Negative Matrix Factorization to Deep Learning

From Non-Negative Matrix Factorization to Deep Learning The Math!! From Non-Negative Matrix Factorization to Deep Learning Intuitions and some Math too! luissarmento@gmailcom https://wwwlinkedincom/in/luissarmento/ October 18, 2017 The Math!! Introduction Disclaimer

More information

Competitive Equilibrium

Competitive Equilibrium Competitive Equilibrium Econ 2100 Fall 2017 Lecture 16, October 26 Outline 1 Pareto Effi ciency 2 The Core 3 Planner s Problem(s) 4 Competitive (Walrasian) Equilibrium Decentralized vs. Centralized Economic

More information

Analysis of Bank Branches in the Greater Los Angeles Region

Analysis of Bank Branches in the Greater Los Angeles Region Analysis of Bank Branches in the Greater Los Angeles Region Brian Moore Introduction The Community Reinvestment Act, passed by Congress in 1977, was written to address redlining by financial institutions.

More information

CS425: Algorithms for Web Scale Data

CS425: Algorithms for Web Scale Data CS: Algorithms for Web Scale Data Most of the slides are from the Mining of Massive Datasets book. These slides have been modified for CS. The original slides can be accessed at: www.mmds.org J. Leskovec,

More information

Click Prediction and Preference Ranking of RSS Feeds

Click Prediction and Preference Ranking of RSS Feeds Click Prediction and Preference Ranking of RSS Feeds 1 Introduction December 11, 2009 Steven Wu RSS (Really Simple Syndication) is a family of data formats used to publish frequently updated works. RSS

More information

Linear Regression Models

Linear Regression Models Linear Regression Models Model Description and Model Parameters Modelling is a central theme in these notes. The idea is to develop and continuously improve a library of predictive models for hazards,

More information

Finding Robust Solutions to Dynamic Optimization Problems

Finding Robust Solutions to Dynamic Optimization Problems Finding Robust Solutions to Dynamic Optimization Problems Haobo Fu 1, Bernhard Sendhoff, Ke Tang 3, and Xin Yao 1 1 CERCIA, School of Computer Science, University of Birmingham, UK Honda Research Institute

More information

COT: Contextual Operating Tensor for Context-Aware Recommender Systems

COT: Contextual Operating Tensor for Context-Aware Recommender Systems Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence COT: Contextual Operating Tensor for Context-Aware Recommender Systems Qiang Liu, Shu Wu, Liang Wang Center for Research on Intelligent

More information

MATH 1150 Chapter 2 Notation and Terminology

MATH 1150 Chapter 2 Notation and Terminology MATH 1150 Chapter 2 Notation and Terminology Categorical Data The following is a dataset for 30 randomly selected adults in the U.S., showing the values of two categorical variables: whether or not the

More information

The Journal of Database Marketing, Vol. 6, No. 3, 1999, pp Retail Trade Area Analysis: Concepts and New Approaches

The Journal of Database Marketing, Vol. 6, No. 3, 1999, pp Retail Trade Area Analysis: Concepts and New Approaches Retail Trade Area Analysis: Concepts and New Approaches By Donald B. Segal Spatial Insights, Inc. 4938 Hampden Lane, PMB 338 Bethesda, MD 20814 Abstract: The process of estimating or measuring store trade

More information

Maximum Margin Matrix Factorization for Collaborative Ranking

Maximum Margin Matrix Factorization for Collaborative Ranking Maximum Margin Matrix Factorization for Collaborative Ranking Joint work with Quoc Le, Alexandros Karatzoglou and Markus Weimer Alexander J. Smola sml.nicta.com.au Statistical Machine Learning Program

More information

Data Science Mastery Program

Data Science Mastery Program Data Science Mastery Program Copyright Policy All content included on the Site or third-party platforms as part of the class, such as text, graphics, logos, button icons, images, audio clips, video clips,

More information

Recommendation Systems

Recommendation Systems Recommendation Systems Pawan Goyal CSE, IITKGP October 29-30, 2015 Pawan Goyal (IIT Kharagpur) Recommendation Systems October 29-30, 2015 1 / 61 Recommendation System? Pawan Goyal (IIT Kharagpur) Recommendation

More information

Application of Indirect Race/ Ethnicity Data in Quality Metric Analyses

Application of Indirect Race/ Ethnicity Data in Quality Metric Analyses Background The fifteen wholly-owned health plans under WellPoint, Inc. (WellPoint) historically did not collect data in regard to the race/ethnicity of it members. In order to overcome this lack of data

More information

Statistics Boot Camp. Dr. Stephanie Lane Institute for Defense Analyses DATAWorks 2018

Statistics Boot Camp. Dr. Stephanie Lane Institute for Defense Analyses DATAWorks 2018 Statistics Boot Camp Dr. Stephanie Lane Institute for Defense Analyses DATAWorks 2018 March 21, 2018 Outline of boot camp Summarizing and simplifying data Point and interval estimation Foundations of statistical

More information

BiCycle: Item Recommendation with Life Cycles

BiCycle: Item Recommendation with Life Cycles : Item Recommendation with Life Cycles Xinyue Liu, Yuanfang Song, Charu Aggarwal, Yao Zhang and Xiangnan Kong Worcester Polytechnic Institute, Worcester, MA, USA University of Wisconsin-Madison, Madison,

More information

Matrix Factorization and Collaborative Filtering

Matrix Factorization and Collaborative Filtering 10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Matrix Factorization and Collaborative Filtering MF Readings: (Koren et al., 2009)

More information

Collaborative Topic Modeling for Recommending Scientific Articles

Collaborative Topic Modeling for Recommending Scientific Articles Collaborative Topic Modeling for Recommending Scientific Articles Chong Wang and David M. Blei Best student paper award at KDD 2011 Computer Science Department, Princeton University Presented by Tian Cao

More information

Wisdom of the Better Few: Cold Start Recommendation via Representative based Rating Elicitation

Wisdom of the Better Few: Cold Start Recommendation via Representative based Rating Elicitation Wisdom of the Better Few: Cold Start Recommendation via Representative based Rating Elicitation Nathan Liu Hong Kong University of Science and Technology nliu@cse.ust.hk Xiangrui Meng Stanford University

More information

Iterative Laplacian Score for Feature Selection

Iterative Laplacian Score for Feature Selection Iterative Laplacian Score for Feature Selection Linling Zhu, Linsong Miao, and Daoqiang Zhang College of Computer Science and echnology, Nanjing University of Aeronautics and Astronautics, Nanjing 2006,

More information

Elver: Recommending Facebook Pages in Cold Start Situation Without Content Features

Elver: Recommending Facebook Pages in Cold Start Situation Without Content Features Elver: Recommending Facebook Pages in Cold Start Situation Without Content Features Yusheng Xie, Zhengzhang Chen, Kunpeng Zhang, Chen Jin, Yu Cheng, Ankit Agrawal, Alok Choudhary Northwestern University

More information

Summary statistics. G.S. Questa, L. Trapani. MSc Induction - Summary statistics 1

Summary statistics. G.S. Questa, L. Trapani. MSc Induction - Summary statistics 1 Summary statistics 1. Visualize data 2. Mean, median, mode and percentiles, variance, standard deviation 3. Frequency distribution. Skewness 4. Covariance and correlation 5. Autocorrelation MSc Induction

More information

SQL-Rank: A Listwise Approach to Collaborative Ranking

SQL-Rank: A Listwise Approach to Collaborative Ranking SQL-Rank: A Listwise Approach to Collaborative Ranking Liwei Wu Depts of Statistics and Computer Science UC Davis ICML 18, Stockholm, Sweden July 10-15, 2017 Joint work with Cho-Jui Hsieh and James Sharpnack

More information

How likely is Simpson s paradox in path models?

How likely is Simpson s paradox in path models? How likely is Simpson s paradox in path models? Ned Kock Full reference: Kock, N. (2015). How likely is Simpson s paradox in path models? International Journal of e- Collaboration, 11(1), 1-7. Abstract

More information

Data Mining and Matrices

Data Mining and Matrices Data Mining and Matrices 08 Boolean Matrix Factorization Rainer Gemulla, Pauli Miettinen June 13, 2013 Outline 1 Warm-Up 2 What is BMF 3 BMF vs. other three-letter abbreviations 4 Binary matrices, tiles,

More information

Analytics for an Online Retailer: Demand Forecasting and Price Optimization

Analytics for an Online Retailer: Demand Forecasting and Price Optimization Analytics for an Online Retailer: Demand Forecasting and Price Optimization Kris Johnson Ferreira Technology and Operations Management Unit, Harvard Business School, kferreira@hbs.edu Bin Hong Alex Lee

More information

Factored Proximity Models for Top-N Recommendations

Factored Proximity Models for Top-N Recommendations Factored Proximity Models for Top- Recommendations Athanasios. ikolakopoulos 1,3, Vassilis Kalantzis 2, Efstratios Gallopoulos 1 and John D. Garofalakis 1 Department of Computer Engineering and Informatics

More information

FUZZY ASSOCIATION RULES: A TWO-SIDED APPROACH

FUZZY ASSOCIATION RULES: A TWO-SIDED APPROACH FUZZY ASSOCIATION RULES: A TWO-SIDED APPROACH M. De Cock C. Cornelis E. E. Kerre Dept. of Applied Mathematics and Computer Science Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium phone: +32

More information

A Bayesian Treatment of Social Links in Recommender Systems ; CU-CS

A Bayesian Treatment of Social Links in Recommender Systems ; CU-CS University of Colorado, Boulder CU Scholar Computer Science Technical Reports Computer Science Spring 5--0 A Bayesian Treatment of Social Links in Recommender Systems ; CU-CS-09- Mike Gartrell University

More information

Algorithm Independent Topics Lecture 6

Algorithm Independent Topics Lecture 6 Algorithm Independent Topics Lecture 6 Jason Corso SUNY at Buffalo Feb. 23 2009 J. Corso (SUNY at Buffalo) Algorithm Independent Topics Lecture 6 Feb. 23 2009 1 / 45 Introduction Now that we ve built an

More information

CIVL 7012/8012. Collection and Analysis of Information

CIVL 7012/8012. Collection and Analysis of Information CIVL 7012/8012 Collection and Analysis of Information Uncertainty in Engineering Statistics deals with the collection and analysis of data to solve real-world problems. Uncertainty is inherent in all real

More information

Detecting Anomalous and Exceptional Behaviour on Credit Data by means of Association Rules. M. Delgado, M.D. Ruiz, M.J. Martin-Bautista, D.

Detecting Anomalous and Exceptional Behaviour on Credit Data by means of Association Rules. M. Delgado, M.D. Ruiz, M.J. Martin-Bautista, D. Detecting Anomalous and Exceptional Behaviour on Credit Data by means of Association Rules M. Delgado, M.D. Ruiz, M.J. Martin-Bautista, D. Sánchez 18th September 2013 Detecting Anom and Exc Behaviour on

More information

Large-scale Collaborative Ranking in Near-Linear Time

Large-scale Collaborative Ranking in Near-Linear Time Large-scale Collaborative Ranking in Near-Linear Time Liwei Wu Depts of Statistics and Computer Science UC Davis KDD 17, Halifax, Canada August 13-17, 2017 Joint work with Cho-Jui Hsieh and James Sharpnack

More information

Data Mining Techniques

Data Mining Techniques Data Mining Techniques CS 622 - Section 2 - Spring 27 Pre-final Review Jan-Willem van de Meent Feedback Feedback https://goo.gl/er7eo8 (also posted on Piazza) Also, please fill out your TRACE evaluations!

More information

Joint user knowledge and matrix factorization for recommender systems

Joint user knowledge and matrix factorization for recommender systems World Wide Web (2018) 21:1141 1163 DOI 10.1007/s11280-017-0476-7 Joint user knowledge and matrix factorization for recommender systems Yonghong Yu 1,2 Yang Gao 2 Hao Wang 2 Ruili Wang 3 Received: 13 February

More information

INFO 4300 / CS4300 Information Retrieval. slides adapted from Hinrich Schütze s, linked from

INFO 4300 / CS4300 Information Retrieval. slides adapted from Hinrich Schütze s, linked from INFO 4300 / CS4300 Information Retrieval slides adapted from Hinrich Schütze s, linked from http://informationretrieval.org/ IR 8: Evaluation & SVD Paul Ginsparg Cornell University, Ithaca, NY 20 Sep 2011

More information

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 12 Marginal Quantity Discount, Multiple Item Inventory Constraint

More information

MultiscaleMaterialsDesignUsingInformatics. S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan AFOSR-FA

MultiscaleMaterialsDesignUsingInformatics. S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan AFOSR-FA MultiscaleMaterialsDesignUsingInformatics S. R. Kalidindi, A. Agrawal, A. Choudhary, V. Sundararaghavan AFOSR-FA9550-12-1-0458 1 Hierarchical Material Structure Kalidindi and DeGraef, ARMS, 2015 Main Challenges

More information

Lecture 3. The Population Variance. The population variance, denoted σ 2, is the sum. of the squared deviations about the population

Lecture 3. The Population Variance. The population variance, denoted σ 2, is the sum. of the squared deviations about the population Lecture 5 1 Lecture 3 The Population Variance The population variance, denoted σ 2, is the sum of the squared deviations about the population mean divided by the number of observations in the population,

More information

Mixed Membership Matrix Factorization

Mixed Membership Matrix Factorization Mixed Membership Matrix Factorization Lester Mackey 1 David Weiss 2 Michael I. Jordan 1 1 University of California, Berkeley 2 University of Pennsylvania International Conference on Machine Learning, 2010

More information

Chapter 3 Multiple Regression Complete Example

Chapter 3 Multiple Regression Complete Example Department of Quantitative Methods & Information Systems ECON 504 Chapter 3 Multiple Regression Complete Example Spring 2013 Dr. Mohammad Zainal Review Goals After completing this lecture, you should be

More information