Emmanuel Frénod. Laboratoire de Mathématiques de Bretagne Atlantique (UMR6205) - Université Bretagne-Sud - Vannes & See-d 1

Transcription

1 Math-Industry Day IHP - Paris November 23th, 2016 Towards new Machine Learning tools based on Ode and Pde models Emmanuel Frénod Laboratoire de Mathématiques de Bretagne Atlantique (UMR6205) - Université Bretagne-Sud - Vannes & See-d 1

2 2 DATA

3 Data Phase Period 1 à à à 43 Lipid proportion 20% 17% 18% Protein proportion 40% 45% 48% Consumption Weight gain

4 Data Phase Period 1 à à à 43 Lipid proportion 20% 17% 18% Phase Protein proportion 40% 1 45% 2 48% 3 Period Consumption à à à Lipid proportion 23% 18% 20% Weight gain Phase 1 2 Protein proportion 36% 47% 46% 3 Period Consumption à à à Lipid proportion Weight gain % % % 965 Protein proportion 36% 47% 46% 4 Consumption Weight gain

5 Machine Learning Objective : Learn to forecast 5 5

6 Machine Learning Objective : Learn to forecast Input ML Tool Output 6 6

7 Machine Learning For our problem Information about Consumption Weight gain Input ML Tool Output Information about Phase Lipid proportion Protein proportion 7 7

8 Machine Learning Generic working Groups Correlations Forecasts Etc. Input ML Tool Output Learning base Characters for learning Characters for tests 8

9 Machine Learning Using Behavior Input ML Tool Output New character 9 9

10 Machine Learning How it works Random Forests Decision Tree Neuron network Deep learning Input ML Tool Output Classification SVM Ar Arma Arima Adjustment 10 10

11 Machine Learning How it works Random Forests Decision Tree Neuron network Deep learning Input ML Tool Output Classification SVM Ar Arma Arima Adjustment 11 11

12 Machine Learning How it works Random Forests Decision Tree Neuron network Deep learning Step 1 : Select potentially pertinent methods Input ML Tool Output Classification SVM Ar Arma Arima Adjustment 12 12

13 Machine Learning How it works Learning base Characters for learning Characters for tests Random Forests Decision Tree Neuron network Deep learning Step 2 : For each method, determine the best parameters Input ML Tool Output Classification SVM Ar Arma Arima Adjustment 13 13

14 Machine Learning How it works Learning base Characters for learning Characters for tests Random Forests Decision Tree Neuron network Deep learning Step 3 : determine the best method Input ML Tool Output Classification SVM Ar Arma Arima Adjustment 14 14

15 Machine Learning Using Behavior Input ML Tool Output New character 15 15

16 Machine Learning Using Behavior Input ML Tool Output New character Uses: The best method With the right parameters

17 Machine Learning For our problem Random Forests Neuron network Information about Consumption Weight gain Input ML Tool Output Information about Phase Lipid proportion Protein proportion Adjustment 17 17

18 Using and update 18 18

19 Using and update Consumption Comprtement Weight gain Input ML Tool Output New feeding plan 19 19

20 Using and update New data : Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids Input ML Tool Output Update of the forecast tool 20 20

21 Data heterogeneity 21 21

22 Data heterogeneity Pb : Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids

23 Data heterogeneity Solutions - 1: Information about Consumption Weight gain Input ML Tool Output Information about Phase Phase duration Lipid proportion Protein proportion For it works : Enough data in each Phase duration category In our problem : not the case 23 23

24 Data heterogeneity Solutions - 2: Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids

25 Data heterogeneity Solutions - 2: Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids

26 Data heterogeneity Solutions - 2: Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids

27 Data heterogeneity Solutions - 2: Input ML Tool Output Update of the forecast tool Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids

28 Data heterogeneity Limitations of implemented solution: Phase Période 1 à à à 43 Proportion de lipides 20% 17% 18% Proportion de protéines 40% 45% 48% Consommation Prise de poids Strong distortion : Doubt about the solution accuracy 28 28

29 Data heterogeneity Limitations of implemented solution: Phase Période 1 à à à à 47 Proportion de lipides 20% 17% 18% 22% Proportion de protéines 40% 45% 48% 42% Consommation Prise de poids 2. different phase number : Solution non implementable 29 29

30 Data heterogeneity What to do? Use mathematical and/or statistical modeling Coupling model-data 30 30

31 31 MODEL

32 Equation for weight and consumption evolution dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) P(t) : Weight at time t C t : Full (since the beginning) food consumption at time t 32 32

33 Equation for weight and consumption evolution Speed of weight gain at time t dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) Protein proportion in the food Lipid proportion in the food Growth limiter Speed of full food increase at time t Food daily consumption 33 33

34 Equation for weight and consumption evolution dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) Parameters 34 34

35 It is an ODE system dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) 35 35

36 It is an ODE system dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) C t = 0 = 0 P t = 0 = Weight at beginning we can solve using R Matlab, Scilab, etc. For given α, β, η and γ 36 36

37 Examples of solutions for given values of α, β, η, γ 37 37

38 38 MODEL - DATA COUPLING

39 Interpretation of the data set according to the model 39 39

40 Interpretation of the data set according to the model L t, Q(t) 40 40

41 Interpretation of the data set according to the model L t, Q(t) dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) 41 41

42 Interpretation of the data set according to the model L t, Q(t) dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) 42 42

43 L t, Q(t) dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) 43 43

44 Adjust α, β, η and γ For each character (i) and each value set of α, β, η and γ Compute P(t) et C(t) Compute P(End of phase 1), C(End of phase 1), P(End of phase 2), etc. Compute (P(End of phase 1) - Real Weight Gain(End of phase 1)) 2 + (C(End of phase 1) - Real Consumption(End of phase 1)) 2 + (P(End of phase 2) - Real Weight Gain(End of phase 2)) 2 +. = D(i) Compute :;9< = D(i) = Fitness(α, β, η, γ) 44 44

45 Adjust α, β, η and γ Using an optimization method: Find (α, β, η, γ) minimizing : Fitness(α, β, η, γ) = :;9< = D(i) Gives: α>, β?, η, γ> 45 45

46 What do we have? dp dt t = α> Q t + β?l t ( η P(t) P(t) γ> ) L(t) γ> dc dt t = η P(t) L(t) C t = 0 = 0 P t = 0 = Weight at beginning Allows computation of the weight and the full consumption at each time 46 46

47 What do we have? Allows computation of the weight and the full consumption at each time 47 47

48 New predictive tool Information about Consumption Weight gain Input New predictive tool Output Information about Phase Lipid proportion Protein proportion dp dt t = α> Q t + β?l t ( η P(t) P(t) γ> ) L(t) γ> dc dt t = η P(t) L(t)

49 New predictive tool Consumption and weight gain each day Input New predictive tool Output Any new feeding plan dp dt t = α> Q t + β?l t ( η P(t) P(t) γ> ) L(t) γ> dc dt t = η P(t) L(t)

50 NEW MACHINE LEARNING TOOL BASED ON ODE DISCRETIZATION 50

51 Machine Learning How it works Random Forests Decision Tree Neuron network Deep learning Input ML Tool Output Classification SVM Ar Arma Arima Adjustment dp dt dc dt P(t) P(t) γ t = α Q t + β L t (η ) L(t) γ t = η P(t) L(t) 51 51

52 Machine Learning How it works Random Forests Decision Tree Neuron network Deep learning Input ML Tool Output Classification SVM Ar Arma Arima Adjustment dp dt t = α> Q t + β?l t ( η P(t) P(t) γ> ) L(t) γ> dc dt t = η P(t) L(t) 52 52

53 53 Thanks for your attention