FUNNEL: Automatic Mining of Spatially Coevolving Epidemics

Transcription

1 FUNNEL: Automatic Mining of Spatially Coevolving Epidemics By Yasuo Matsubara, Yasushi Sakurai, Willem G. van Panhuis, and Christos Faloutsos SIGKDD 2014 Presented by Sarunya Pumma

2 This presentation has been modified from a presentation slide from SIGKDD 2014 Link to the presentation:

3 Outline Introduction & motivation Problem definition Epidemic modeling using FUNNEL With a single epidemic With multi-evolving epidemics Optimization algorithm Experiments and results Conclusion

4 Introduction & Motivation

5 Introduction & Motivation Given a large set of epidemiological data Shocks (in 1941) Vaccine effect Yearly periodicity Measles cases in the U.S. (number of infectious per week) How to find a model that can represent it efficiently?

6 Introduction & Motivation Considering some existing models The SI model Pros Use a few number of parameters Can capture the dynamics of epidemiological data Cons Cannot represent periodic patterns Cannot use for predicting a future trend S R I Recall a general SIR model Picture reference:

7 Introduction & Motivation Considering some existing models The auto regression (AR) model Pros Use a few number of parameters Cons Cannot model the non-linear patterns (i.e. virus propagation) Non-linear pattern Picture reference:

8 Introduction & Motivation Considering some existing models The PARAFAC model (a generalization of PCA) Pros Use a few number of parameters Cons Cannot handle missing values A graphical representation of a twocomponent PARAFAC model of the data array X Picture reference:

9 Introduction & Motivation They proposed FUNNEL A model for describing non-linear dynamics in coevolving epidemics Properties Sense-making: it can describe the seasonality of diseases, vaccination, and external shocks Fully automatic: it is parameter-free and be able to handle missing/mistake values. No human interaction required Scalable: it scales linearly with the input size Generality: it can be applied to many types of epidemic data

10 Problem Definition

11 Data Description Project Tycho provides infectious diseases data in the U.S. 50 states 56 diseases d l x X n 1888 Time (weekly) (> 125 years) x is number of cases (infectious) e.g. ( measles, NY, April 1-7, 1931, 4000 )

12 Problem Definition Given: Tensor X (disease x state x time) X Find: Compact representation of X X = FUNNEL P1 P2 P3 P4 P5 Pi is property i

13 Problem Definition Important properties of epidemics P1 - yearly periodicity P2 - disease reduction effects P3 - area specificity and sensitivity P4 - external shock events P5 - mistakes, incorrect values

14 Problem Definition P1 - Yearly periodicity Radius: seasonality strength Angle: peak season Spring Summer Winter Fall

15 Problem Definition P1 - Yearly periodicity Radius: seasonality strength Angle: peak season Spring Summer Influenza (peak in cold season) Winter Fall

16 Problem Definition P1 - Yearly periodicity Radius: seasonality strength Angle: peak season Spring Summer Measles (peak in spring) Winter Fall

17 Problem Definition P1 - Yearly periodicity Radius: seasonality strength Angle: peak season Spring Summer Winter Lyme-disease (peak in summer) Fall

18 Problem Definition P1 - Yearly periodicity Radius: seasonality strength Angle: peak season Spring Gonorrhea (STD) (no peak season) Summer Winter Fall

19 Problem Definition P2 - Disease reduction effects Vaccine licensure in 1963

20 Problem Definition P3 - Area specificity and sensitivity Potential population of susceptible for measles PA NY CA TX

21 Problem Definition P4 - External shock events Large outbreaks of measles

22 Problem Definition P5 - Mistakes, incorrect values (Typo)

23 Epidemic Modeling using FUNNEL

24 FUNNEL with a Single Epidemic FUNNEL-BASE where Amplitude of the fluctuation Phase shift of the seasonal cycle Pp = 52, N = S(t) + I(t) + V(t), Average of rate β over the year Number of weeks in a year S(1) = N - 1, I(1) = 1, V(1) = 0 b = {N, β0, δ, γ, Pa, Ps}

25 FUNNEL with a Single Epidemic FUNNEL-R (with disease reduction) where Starting time of disease reduction effect Reduction rate Diffusion rate of the disease reduction effect r = {t θ, θ0}

26 FUNNEL with a Single Epidemic FUNNEL-RE (with disease reduction and external shocks) where Total number of events Temporal susceptible rate Strength of the external shock Duration of the event e (T) = {tμ, t σ, ε0 } Central time point of the external shock event

27 FUNNEL with Multi-Evolving Epidemics Find: Compact representation of X FUNNEL F = {B, R, N, E, M} disease d l states X n time = FUNNEL Global view N B R E M P1 P2 P3 P4 P5 Global view Local view Extra view Extra view Seasonality Reduction P1 P2 bi = {Ni, β0i, δi, γi, Pai, Psi}, bi ϵ B ri = {t θi, θ0i}, ri ϵ R i is a disease ID

28 FUNNEL with Multi-Evolving Epidemics Find: Compact representation of X FUNNEL F = {B, R, N, E, M} disease d l states X n time = FUNNEL N B R E M P1 P2 P3 P4 P5 Global view Global view Local view Extra view Extra view Locality P3 Nij = Sij(t) + Iij(t) + Vij(t) i is a disease ID j is a state ID

29 FUNNEL with Multi-Evolving Epidemics Find: Compact representation of X FUNNEL F = {B, R, N, E, M} disease d l states P4 X n time External shocks = FUNNEL B Global view R N P1 P2 P3 P4 P5 Global view Local view E Recall: temporal susceptible rate Extra view M Extra view E = We replace e (T) in the full model with e (S) to consider l individual location

30 FUNNEL with Multi-Evolving Epidemics Find: Compact representation of X FUNNEL F = {B, R, N, E, M} disease d l states X n time = FUNNEL Global view N B R E M P1 P2 P3 P4 P5 Global view Local view Extra view Extra view Mistake values P5 M is a 3rd-order tensor of mistake data points (a very sparse tensor)

31 Optimization Algorithm

32 Optimization Algorithm The optimization follows the minimum description length (MDL) principle Objective: minimize the size of data by compressing it Objective function: cost of model description (spacewise) Data compression: Huffman coding with a Gaussian distribution is adopted

33 Optimization Algorithm Multi-layer optimization Global-fit is F G = {B, R, E (D), E (T), M (D), M (T) } Local-fit is F L = {N, E (S), M (S) } Levenlerg-Marquardt (LM) is adopted to minimize the cost function

34 Experiments and Results

35 Mumps (Seasonality Disease)

36 Local-Level Fittings for Measles

37 External-Shock Effects

38 Missing Data and Incorrect Data Point Effects

39 Model Accuracy

40 Model Scalability

41 Forecasting Train data: 2/3 Forecast: 1/3

42 Apply to Other Applications Computer virus outbreaks!

43 Conclusion

44 Conclusion FUNNEL is an efficient model for representing epidemic dynamics It can capture yearly-periodicity, epidemic reduction, and local sensitivity efficiently It is fully automatic and highly scalable It can handle missing/wrong data effectively It is general which can be applied to various domains

45 Thank you for your attention

46 Dynamic Poisson Autoregression for Influenza-Like-Illness Case Count Prediction By Zheng Wang, Prithwish Chakrabortty, Sumiko R. Mekaru, John S. Brownstein, Jieping Ye, Naren Ramakrishnan KDD 2015 Presented by Sarunya Pumma

47 Outline Introduction & motivation Case count forecasting ARX model for time series prediction Dynamic ARX model Dynamic Poisson ARX model Experiments and results Conclusion

48 Introduction & Motivation

49 Introduction & Motivation Influenza-like-illness (ILI) is the most common disease Example of Influenza-like-illness case count Goal: predicting characteristics of ILI Seasonal characteristics Overall shape of ILI counts for a specific season (e.g., peak value, peak size Short-term characteristics Absolute values of next data points Picture reference:

50 Introduction & Motivation Existing works SEIR and SIRS Curve simulations with network-based models Filtering -based methods Existing indicator sources Online indicator (Google Flu Trend, Wikipedia, Twitter, etc.) Weather Existing works used the same model to predict influenza for the entire season Characteristics of influenza are different in the peak-season and off-season

51 Introduction & Motivation Proposed work A time series model for predicting short-term characteristics of ILI by using external factors from indicator sources Overview of the model Base model is autoregressive exogenous model (ARX) Models are built separately for each time point To model activities of the disease that evolve over time Models share common characteristics Block coordinate descent is used to fit the model

52 Case Count Forecasting

53 ARX Model for Time Series Prediction General ARX model error yt = F(yt-1, yt-2, yt-3,, xt-1, xt-2, xt-3) + εt variable of interest external variable

54 ARX Model for Time Series Prediction General ARX model weight of the target variables weight of the exogenous variables where p and b are previous time steps

55 ARX Model for Time Series Prediction Compact form where We would like to minimize the least square loss

56 Dynamic ARX Model We build a model for each time point Model similarity graph Node is the model (wt) at each time point Edge is a similarity between 2 models

57 Dynamic ARX Model Model similarity graph with different prior knowledge Fully connected nearest neighbors seasonal nearest neighbors

58 Dynamic ARX Model Adding a similarity measure (Euclidean distance) to the ARX model model similarity Solve a regression problem by using the block coordinate descent optimization

59 Dynamic Poisson ARX Model Since we predict the infected people at different time points, we formulate the problem as Poisson regression Likelihood function From the link function we get

60 Dynamic Poisson ARX Model We maximize the log-likelihood to train weights We can get from the identity link function Then we get our final model

61 Experiment and Results

62 Datasets Reference source: PAHO/CDC US and 14 Latin American countries Weekly count From Jan 1, 2010 to Oct 8, 2014 Physical indicators 5 weather attributes (absolute/relative/specific humidity, precipitation, and temperature) Social indicators Google Flu Trends Google Search Treands HealthMap

63 Evaluation Measures Prediction error actual value predicted value number of time points Prediction Score is 4 - error (a perfect score is 4)

64 Model Similarity

65 Model Similarity Fully connected nearest neighbors seasonal nearest neighbors

66 Forecasting Results Training data First 50 time points Time step settings p = 1 (target variables) and b = 15 (exogenous params) Result DPARX can yield better prediction accuracy than others

67 Seasonal Analysis They calculated the short-term predictions in multiple steps and fitted the curve to get seasonal prediction

68 Conclusion

69 Conclusion DPARX can predict a number ILI cases at a desire time point DPARX extends the original ARX by having a dynamic term based on the similarity between models DPARX can also efficiently reflect the seasonal characteristics of ILI

70 Thank you for your attention