Interpretable deep learning for healthcare
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발표일: 2018.1. 발표자: 최윤재 (Edward Choi, Georgia Tech 박사과정) Since 2012, deep learning, or representation learning has shown impressive progress in computer vision, speech recognition, and natural language processing. The power of deep learning comes from combining expressive models with large labeled data. This allowed the machine to extract useful information from high-dimensional data, which was a human responsibility before the rise of deep learning. Massive data have been collected in healthcare since the introduction of electronic healthcare records (EHR), and the amount of data is more than human medical experts can process. It is expected that, in this regard, deep learning can play a significant role in healthcare as it did in vision and language. However, computational healthcare requires predictive models to be both accurate and interpretable. My talk will introduce how to use recurrent neural networks (RNN), one of the building blocks in deep learning, to process longitudinal EHR data and predict a future event. Specifically, I will focus on predicting a heart failure onset given a patients’ 18 months record. Building on top of this, I will address the interpretability issue of deep learning models, and propose a method to make predictions that is both accurate and interpretable.
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Interpretable deep learning for healthcare
- 2. Index • Healthcare & Machine Learning • Sequence Prediction with RNN • Attention mechanism & interpretable prediction • Proposed model: RETAIN • Experiments & results • Conclusion 2
- 4. SunLab & Healthcare • SunLab & Collaborators ProviderGovernment University Company 4
- 5. SunLab Healthcare Projects • Predictive analytics pipeline & Bayesian optimization • Patient phenotyping • Treatment recommendation • Epilepsy patient prediction • Heart failure prediction • Disease progression modeling 5
- 6. SunLab Healthcare Projects • Predictive analytics pipeline & Bayesian optimization • Patient phenotyping • Treatment recommendation • Epilepsy patient prediction • Heart failure prediction • Disease progression modeling 6
- 7. SunLab Healthcare Projects • Predictive analytics pipeline & Bayesian optimization • Patient phenotyping • Treatment recommendation • Epilepsy patient prediction • Heart failure prediction • Disease progression modeling 7 Observation Window Diagnosis Date Prediction Window Index Date Time
- 8. SunLab Healthcare Projects • Predictive analytics pipeline & Bayesian optimization • Patient phenotyping • Treatment recommendation • Epilepsy patient prediction • Heart failure prediction • Disease progression modeling 8 Cough Visit 1 Fever Fever Visit 2 Chill Fever Visit 3 Pneumonia Chest X-ray Tylenol IV fluid
- 9. SunLab Healthcare Projects • Predictive analytics pipeline & Bayesian optimization • Patient phenotyping • Treatment recommendation • Epilepsy patient prediction • Heart failure prediction • Disease progression modeling 9 Recurrent Neural Network (RNN)
- 11. Sequence Prediction - NLP • Given a sequence of symbols, predict a certain outcome. • Is the given sentence positive or negative ? • “Justice” “League” “is” “as” “impressive” “as” “a” “preschool” “Christmas” “play” • Each word is a symbol • Outcome: 0, 1 (binary) • The sentence is either positive or negative. 11
- 12. Sequence Prediction - EHR • Given a sequence of symbols, predict a certain outcome. • Given a diagnosis history, will the patient have heart failure? • Hypertension, Hypertension, Diabetes, CKD, CKD, Diabetes, MI • Each diagnosis is a symbol • Outcome: 0, 1 (binary) • Either you have HF, or you don’t 12
- 13. What is sequence prediction? • Given a sequence of symbols, predict a certain outcome. • Where is the boundary between exons and introns in the DNA sequence? • What is the French translation of the given English sentence? • Given a diagnosis history, what will he/she have in the next visit? 13
- 14. Sequence prediction with MLP • Let’s start with a simple Multi-layer Perceptron (MLP) • Sentiment classification (positive or negative?) • “justice leagues was as impressive as a preschool christmas play” 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, … x (a vector with 1M elements. One for each word) boy cat justice preschool fun 14
- 15. Sequence prediction with MLP • Let’s start with a simple Multi-layer Perceptron (MLP) • Sentiment classification (positive or negative?) Input Layer x Hidden Layer h x (a vector with 1M elements. One for each word) h = 𝝈(Wh Tx) (transform x for an easier prediction) 15
- 16. Sequence prediction with MLP • Let’s start with a simple Multi-layer Perceptron (MLP) • Sentiment classification (positive or negative?) Input Layer x Hidden Layer h Output y x (a vector with 1M elements. One for each word) h = 𝝈(Wh Tx) (transform x for an easier prediction) y = 𝝈(wo Th) (generate an outcome 0.0~1.0) 16
- 17. Sequence prediction with MLP • Let’s start with a simple Multi-layer Perceptron (MLP) • Sentiment classification (positive or negative?) Input Layer x Hidden Layer h Output y x (a vector with 1M elements. One for each word) h = 𝝈(Wh Tx) (transform x for an easier prediction) y = 𝝈(wo Th) (generate an outcome 0.0~1.0) 17
- 18. Sequence prediction with RNN • Now let’s use Recurrent Neural Network (RNN) • Same sentiment classification (positive or negative?) Hidden Layer h1 h1= 𝝈(Wi Tx1) x1 (a vector with 1M elements. Only “justice” is 1.) 18 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, … justice
- 19. Sequence prediction with RNN • Let’s use RNN now • Same sentiment classification (positive or negative?) h2 League h1 Justice x1 x2 h2= 𝝈(Wh Th1 + Wi Tx2) 19
- 20. Sequence prediction with RNN • Let’s use RNN now • Same sentiment classification (positive or negative?) h9 h10 h2 League Christmas play h1 Justice x1 x2 x9 x10 h10= 𝝈(Wh Th9 + Wi Tx10) 20
- 21. Sequence prediction with RNN • Let’s use RNN now • Same sentiment classification (positive or negative?) h10 Output y = 𝝈(wo Th10) Outcome 0.0 ~ 1.0 21
- 22. Sequence prediction with RNN • Let’s use RNN now • Same sentiment classification (positive or negative?) h10 Output y = 𝝈(wo Th10) Outcome 0.0 ~ 1.0 22
- 23. Limitation of RNN • Transparency • RNN is a blackbox • Feed input, receive output • Hard to tell what caused the outcome 23
- 24. Limitation of RNN • Transparency • RNN is a blackbox • Feed input, receive output • Hard to tell what caused the outcome • Outcome 0.9 • Was it because of “Justice”? • Was it because of “impressive”? • Was it because of “Christmas”? 24
- 25. Limitation of RNN • Transparency • RNN is a blackbox • Feed input, receive output • Hard to tell what caused the outcome h9 h10 h2 League Christmas play h1 Justice All inputs accumulated here 25
- 27. Attention models • Bahdanau, Cho, Bengio, 2014 • English-French translation using RNN • Let’s use hidden layers from all timesteps to make predictions 27
- 28. Attention models • Bahdanau, Cho, Bengio, 2014 • English-French translation using RNN • Let’s use hidden layers from all timesteps to make predictions h9 h10 h2 League Christmas play h1 Justice 28
- 29. Attention models • Bahdanau, Cho, Bengio, 2014 • English-French translation using RNN • Let’s use hidden layers from all timesteps to make predictions h9 h10 h2 League Christmas play h1 Justice c 𝛼# 𝛼$ 𝛼% 𝛼#& 𝛼# + 𝛼$ + ⋯ + 𝛼#& = 1 𝒄 = 𝛼# 𝒉# + 𝛼$ 𝒉$ + ⋯ + 𝛼#& 𝒉#& 29
- 30. Attention models • Bahdanau, Cho, Bengio, 2014 • English-French translation using RNN • Let’s use hidden layers from all timesteps to make predictions Outputc 𝛼# 𝛼$ 𝛼% 𝛼#& y = 𝝈(wo Tc) h9 h10 h2 League Christmas play h1 Justice 30
- 32. Attention models • Attention, what is it good for? • c is an explicit combination of all past information • 𝛼#, 𝛼$, ⋯ , 𝛼#& denote the usefulness from each word • We can tell which word was used the most/least to the outcome c 𝛼# 𝛼$ 𝛼% 𝛼#& 32
- 33. Attention models • Attention, what is it good for? • Now c is an explicit combination of all past information • 𝛼#, 𝛼$, ⋯ , 𝛼#& denote the usefulness from each word • We can tell which word was used the most/least to the outcome • Attentions 𝛼. are generated using an MLP c 𝛼# 𝛼$ 𝛼% 𝛼#& 33
- 34. Attention Example • English-French translation • Bahdanau, Cho, Bengio 2014 (a) (c) Figure3:FoursamplealignmentsfoundbyRN correspondtothewordsinthesourcesentence( respectively.Eachpixelshowstheweight↵ijoft targetword(seeEq.(6)),ingrayscale(0:black, randomlyselectedsamplesamongthesentencesw 10and20wordsfromthetestset. Oneofthemotivationsbehindtheproposedappr inthebasicencoder–decoderapproach.Wecon encoder–decoderapproachtounderperformwith manceofRNNencdecdramaticallydropsasthelen bothRNNsearch-30andRNNsearch-50aremore 50,especially,showsnoperformancedeterioratio superiorityoftheproposedmodeloverthebasic 34
- 36. Structure of EHR • Assumption so far • Word sequence = Dx sequence • Justice, League, is, as, impressive, as, … • Cough, Benzonatate, Fever, Pneumonia, Chest X-ray, Amoxicillin, ... 36
- 37. Structure of EHR • Assumption so far • Word sequence = Dx sequence • Justice, League, is, as, impressive, as, … • Cough, Benzonatate, Fever, Pneumonia, Chest X-ray, Amoxicillin, ... Cough Benzonatate Fever Pneumonia Amoxicillin Chest X-ray Time 37
- 38. Structure of EHR • Assumption so far • Word sequence = Dx sequence • Justice, League, is, as, impressive, as, … • Cough, Benzonatate, Fever, Pneumonia, Chest X-ray, Amoxicillin, ... Cough Benzonatate Fever Pneumonia Amoxicillin Chest X-ray Time 38
- 39. Structure of EHR • Assumption so far • Word sequence = Dx sequence • Justice, League, is, as, impressive, as, … • Cough, Benzonatate, Fever, Pneumonia, Chest X-ray, Amoxicillin, ... Cough Visit 1 Fever Fever Visit 2 Chill Fever Visit 3 Pneumonia Chest X-ray Tylenol IV fluid 39
- 40. Straightforward RNN for EHR • RNN now accepts multiple medical codes at each timestep (i.e. visit) 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, … x1 (First visit vector with 40K elements. One for each medical code) cough fever tylenol pneumonia 40 Cough Visit 1 Fever Tylenol IV fluid
- 41. Straightforward RNN for EHR • RNN now accepts multiple medical codes at each timestep (aka visit) Input Layer x1 Embedding Layer v1 x1 (a multi-hot vector with 40K elements. One for each code) v1 = tanh(Wv Tx1) (Transform x to a compact representation) 41
- 42. Straightforward RNN for EHR • RNN now accepts multiple medical codes at each timestep (aka visit) Input Layer x1 Embedding Layer v1 x1 (a multi-hot vector with 40K elements. One for each code) v1 = tanh(Wv Tx1) (Transform x to a compact representation) Hidden Layer h1 h1= 𝝈(Wi Tv1) 42
- 45. Straightforward RNN for EHR • RNN now accepts multiple medical codes at each timestep (aka visit) Hidden Layer hT Output y = 𝝈(wo ThT) Outcome 0.0 ~ 1.0 45
- 47. RETAIN: Motivation • Within a single visit, which code contributes more to the prediction? v1 Hidden Layer h1 v2 Hidden Layer h2 vT Hidden Layer hT 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, … cough fever tylenol pneumonia 47
- 48. RETAIN: Design Choices 48 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN
- 49. RETAIN: Design Choices 49 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN MLP embeds the visitsRNN embeds the visits
- 50. RETAIN: Design Choices 50 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN RNN generates attention for the visits MLP generates attentions for the visits
- 51. RETAIN: Design Choices 51 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN Another RNN generates attentions for the codes within each visit
- 52. RETAIN: Design Choices 52 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN Visits are combined for prediction Visits are combined for prediction
- 53. RETAIN: Design Choices 53 "# $# %# &# ⨀ (# "# $# %# &# ⨀ (# )# *# Standard attention model RETAIN Less interpretable end-to-end Interpretable end-to-end
- 54. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict54
- 55. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict55 an RNN. To find the j-th word in the target language, we generate attentions ↵i word in the original sentence. Then, we compute the context vector cj = P i ↵j i hi j-th word in the target language. In general, the attention mechanism allows the mo word (or words) in the given sentence when generating each word in the target lan In this work, we define a temporal attention mechanism to provide interpreta healthcare. Doctors generally pay attention to specific clinical information (e.g., k timing when reviewing EHR data. We exploit this insight to develop a temporal atte doctors’ practice, which will be introduced next. 2.2 Reverse Time Attention Model RETAIN Figure 2 shows the high-level overview of our model. One key idea is to delegate a the prediction responsibility to the attention weights generation process. RNNs bec due to the recurrent weights feeding past information to the hidden layer. Theref visit-level and the variable-level (individual coordinates of xi) influence, we use a input vector xi. That is, we define vi = Exi, where vi 2 Rm denotes the embedding of the input vector xi 2 Rr , m the size of t E 2 Rm⇥r the embedding matrix to learn. We can easily choose a more sophisticat
- 56. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict where vi 2 Rm denotes the embedding of the input vector xi 2 Rr , m th100 dimension, Wemb 2 Rm⇥r the embedding matrix to learn. We can easily cho101 but still interpretable representation such as multilayer perceptron (MLP)102 used for representation learning in EHR data [10].103 We use two sets of weights for the visit-level attention and the variable-lev104 The scalars ↵1, . . . , ↵i are the visit-level attention weights that govern th105 embedding v1, . . . , vi. The vectors 1, . . . , i are the variable-level attenti106 each coordinate of the visit embedding v1,1, v1,2, . . . , v1,m, . . . , vi,1, vi,2, .107 We use two RNNs, RNN↵ and RNN , to separately generate ↵’s and ’s a108 gi, gi 1, . . . , g1 = RNN↵(vi, vi 1, . . . , v1), ej = w> ↵ gj + b↵, for j = 1, . . . , i ↵1, ↵2, . . . , ↵i = Softmax(e1, e2, . . . , ei) hi, hi 1, . . . , h1 = RNN (vi, vi 1, . . . , v1) j = tanh W hj + b for j = 1, where gi 2 Rp is the hidden layer of RNN↵ at time step i, hi 2 Rq the109 at time step i and w↵ 2 Rp , b↵ 2 R, W 2 Rm⇥q and b 2 Rm are110 The hyperparameters p and q determine the hidden layer size of RNN↵ a111 3 56
- 57. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict mb 2 R the embedding matrix to learn. We can easily choose a more sophisticated table representation such as multilayer perceptron (MLP) [13, 29] which has been ntation learning in EHR data [10]. of weights for the visit-level attention and the variable-level attention, respectively. . . . , ↵i are the visit-level attention weights that govern the influence of each visit . . , vi. The vectors 1, . . . , i are the variable-level attention weights that focus on of the visit embedding v1,1, v1,2, . . . , v1,m, . . . , vi,1, vi,2, . . . , vi,m. Ns, RNN↵ and RNN , to separately generate ↵’s and ’s as follows, gi, gi 1, . . . , g1 = RNN↵(vi, vi 1, . . . , v1), ej = w> ↵ gj + b↵, for j = 1, . . . , i ↵1, ↵2, . . . , ↵i = Softmax(e1, e2, . . . , ei) (Step 2) hi, hi 1, . . . , h1 = RNN (vi, vi 1, . . . , v1) j = tanh W hj + b for j = 1, . . . , i, (Step 3) is the hidden layer of RNN↵ at time step i, hi 2 Rq the hidden layer of RNN nd w↵ 2 Rp , b↵ 2 R, W 2 Rm⇥q and b 2 Rm are the parameters to learn. meters p and q determine the hidden layer size of RNN↵ and RNN , respectively. 3 57
- 58. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict records, they typically study the patient’s most recent records first, and go back in time. ationally, running the RNN in reversed time order has several advantages as well: The reverse der allows us to generate e’s and ’s that dynamically change their values when making ons at different time steps i = 1, 2, . . . , T. It ensures that the attention vectors will be different timestamp and makes the attention generation process computationally more stable.1 erate the context vector ci for a patient up to the i-th visit as follows, ci = iX j=1 ↵j j vj, (Step 4) denotes element-wise multiplication. We use the context vector ci 2 Rm to predict the true 2 {0, 1}s as follows, byi = Softmax(Wci + b), (Step 5) W 2 Rs⇥m and b 2 Rs are parameters to learn. We use the cross-entropy to calculate the ation loss as follows, L(x1, . . . , xT ) = 1 N NX n=1 1 T(n) T (n) X i=1 ⇣ y> i log(byi) + (1 yi)> log(1 byi) ⌘ (1) we sum the cross entropy errors from all dimensions of byi. In case of real-valued output , we can change the cross-entropy in Eq. (1) to for example mean squared error. our attention mechanism can be viewed as the inverted architecture of the standard attention ism for NLP [2] where the words are encoded using RNN and generate the attention weights 58
- 59. RETAIN: Model Architecture ,# ,) ,* &# &) &* "# ") "* $# $) $* +# +) +* '# ') '* Σ .* /* 5 ⨀ ⨀ ⨀ 1 23 4 011& 0112 Time ure 2: Unfolded view of RETAIN’s architecture: Given input sequence x1, . . . , xi, we predict ci = iX j=1 ↵j j vj, where denotes element-wise multiplication. We use the context vector ci 2123 label yi 2 {0, 1}s as follows,124 byi = Softmax(Wci + b), where W 2 Rs⇥m and b 2 Rs are parameters to learn. We use the cross-en125 classification loss as follows,126 L(x1, . . . , xT ) = 1 N NX n=1 1 T(n) T (n) X i=1 ⇣ y> i log(byi) + (1 yi)> log where we sum the cross entropy errors from all dimensions of byi. In case127 yi 2 Rs , we can change the cross-entropy in Eq. (1) to for example mean squ128 Overall, our attention mechanism can be viewed as the inverted architecture of129 mechanism for NLP [2] where the words are encoded using RNN and generate130 using MLP. Our method, on the other hand, uses MLP to embed the visit in131 interpretation and uses RNN to generate two sets of attention weights, reco132 information as well as mimicking the behavior of physicians.133 59
- 60. RETAIN: Calculating the Contributions e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the 60
- 61. RETAIN: Calculating the Contributions the past records, they typically study the patient’s most recent records fi117 Computationally, running the RNN in reversed time order has several advan118 time order allows us to generate e’s and ’s that dynamically change th119 predictions at different time steps i = 1, 2, . . . , T. It ensures that the attentio120 at each timestamp and makes the attention generation process computation121 We generate the context vector ci for a patient up to the i-th visit as follow122 ci = iX j=1 ↵j j vj, where denotes element-wise multiplication. We use the context vector ci123 label yi 2 {0, 1}s as follows,124 byi = Softmax(Wci + b), where W 2 Rs⇥m and b 2 Rs are parameters to learn. We use the cross125 classification loss as follows,126 L(x1, . . . , xT ) = 1 N NX n=1 1 T(n) T (n) X i=1 ⇣ y> i log(byi) + (1 yi)> where we sum the cross entropy errors from all dimensions of byi. In ca127 yi 2 Rs , we can change the cross-entropy in Eq. (1) to for example mean128 Overall, our attention mechanism can be viewed as the inverted architecture129 mechanism for NLP [2] where the words are encoded using RNN and gene130 e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the 61 n terms of the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the argest change in yi,d will be the input variable with highest contribution. More formally, given the equence x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which an be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) where ci 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings 1, . . . , vi weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) Using the fact that the visit embedding vi is the sum of the columns of Wemb weighted by each lement of xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) where xj,k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the kelihood of yi can be completely deconstructed down to the variables at each input x1, . . . , xi. herefore we can calculate the contribution ! of the k-th variable of the input xj at time step j i,
- 62. RETAIN: Calculating the Contributions n terms of the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the argest change in yi,d will be the input variable with highest contribution. More formally, given the equence x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which an be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) where ci 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings 1, . . . , vi weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) Using the fact that the visit embedding vi is the sum of the columns of Wemb weighted by each lement of xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) where xj,k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the kelihood of yi can be completely deconstructed down to the variables at each input x1, . . . , xi. herefore we can calculate the contribution ! of the k-th variable of the input xj at time step j i, e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the 62 2.2 Reverse Time Attention Model RETAIN Figure 2 shows the high-level overview of our model. One key idea is the prediction responsibility to the attention weights generation proces due to the recurrent weights feeding past information to the hidden l visit-level and the variable-level (individual coordinates of xi) influen input vector xi. That is, we define vi = Exi, where vi 2 Rm denotes the embedding of the input vector xi 2 Rr , m E 2 Rm⇥r the embedding matrix to learn. We can easily choose a mor representation such as multilayer perceptron (MLP) [13, 28] which has in EHR data [10]. We use two sets of weights for the visit-level attention and the vari scalars ↵1, . . . , ↵i are the visit-level attention weights that govern th v1, . . . , vi. The vectors 1, . . . , i are the variable-level attention weig the visit embedding v1,1, v1,2, . . . , v1,m, . . . , vi,1, vi,2, . . . , vi,m. We use two RNNs, RNN↵ and RNN , to separately generate ↵’s a predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5) k-th column of E
- 63. RETAIN: Calculating the Contributions e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the Inside the iteration over k 63 e in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the largest change in e the input variable with highest contribution. More formally, given the sequence x1, . . . , xi, we are predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, n be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(y , x ) = ↵ W( e ) x , (5) n terms of the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the argest change in yi,d will be the input variable with highest contribution. More formally, given the equence x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which an be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) where ci 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings 1, . . . , vi weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) Using the fact that the visit embedding vi is the sum of the columns of Wemb weighted by each lement of xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) where xj,k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the kelihood of yi can be completely deconstructed down to the variables at each input x1, . . . , xi. herefore we can calculate the contribution ! of the k-th variable of the input xj at time step j i, predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5) Scalars in the front
- 64. RETAIN: Calculating the Contributions e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the 64 1 i predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, n be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5) n terms of the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the argest change in yi,d will be the input variable with highest contribution. More formally, given the equence x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which an be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) where ci 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings 1, . . . , vi weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) Using the fact that the visit embedding vi is the sum of the columns of Wemb weighted by each lement of xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) where xj,k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the kelihood of yi can be completely deconstructed down to the variables at each input x1, . . . , xi. herefore we can calculate the contribution ! of the k-th variable of the input xj at time step j i, predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5)
- 65. RETAIN: Calculating the Contributions e a method to interpret the end-to-end behavior of RETAIN. By keeping ↵ and values fixed ntion of doctors, we will analyze the changes in the probability of each label yi,1, . . . , yi,s f the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the ange in yi,d will be the input variable with highest contribution. More formally, given the x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which pressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of Wemb weighted by each f xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the Contribution of the k-th code in the j-th visit 65 p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) e visit embedding vi is the sum of the columns of E weighted by each element of xi, en as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of econstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5) i is omitted in the ↵j and j. As we have described in Section 2.2, we are generating 1 i predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, n be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5) n terms of the change in an original input x1,1, . . . , x1,r, . . . , xi,1, . . . , xi,r. The xj,k that lead to the argest change in yi,d will be the input variable with highest contribution. More formally, given the equence x1, . . . , xi, we are trying to predict the probability of the output vector yi 2 {0, 1}s , which an be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) where ci 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings 1, . . . , vi weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) Using the fact that the visit embedding vi is the sum of the columns of Wemb weighted by each lement of xi, Eq (3) can be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,kWemb[:, k] ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j Wemb[:, k] ⌘ + b ◆ (4) where xj,k is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the kelihood of yi can be completely deconstructed down to the variables at each input x1, . . . , xi. herefore we can calculate the contribution ! of the k-th variable of the input xj at time step j i, predict the probability of the output vector yi 2 {0, 1}s , which can be expressed as follows p(yi|x1, . . . , xi) = p(yi|ci) = Softmax (Wci + b) (2) 2 Rm denotes the context vector. According to Step 4, ci is the sum of the visit embeddings weighted by the attentions ↵’s and ’s. Therefore Eq (2) can be rewritten as follows, p(yi|x1, . . . , xi) = p(yi|ci) = Softmax ✓ W ⇣ iX j=1 ↵j j vj ⌘ + b ◆ (3) fact that the visit embedding vi is the sum of the columns of E weighted by each element of xi, be rewritten as follows, p(yi|x1, . . . , xi) = Softmax ✓ W ⇣ iX j=1 ↵j j rX k=1 xj,ke:,k ⌘ + b ◆ = Softmax ✓ iX j=1 rX k=1 xj,k ↵jW ⇣ j e:,k ⌘ + b ◆ (4) is the k-th element of the input vector xj. Eq (4) tells us that the calculation of the likelihood of completely deconstructed down to the variables at each input x1, . . . , xi. Therefore we can calculate bution ! of the k-th variable of the input xj at time step j i, for predicting yi as follows, !(yi, xj,k) = ↵jW( j e:,k) | {z } Contribution coefficient xj,k |{z} Input value , (5)
- 67. Heart Failure (HF) Prediction • Objective • Given a patient record, predict whether he/she will be diagnosed with HF in the future • 34K patients from Sutter PAMF • 4K cases, 30K controls • Use 18-months history before being diagnosed with HF • Number of medical codes • 283 diagnosis codes • 96 medication codes • 238 procedure codes 67 617 medical codes
- 68. Heart failure prediction • Performance measure • Area under the ROC curve (AUC) • Competing models • Logistic regression • Aggregate all past codes into a fixed-size vector. Feed it to LR • MLP • Aggregate all past codes into a fixed-size vector. Feed it to MLP • Two-layer RNN • Visits are fed to the RNN, whose hidden layers are fed to another RNN. • RNN+attention (Bahdanau et al. 2014) • Visits are fed to RNN. Visit-level attentions are generated by MLP • RETAIN 68
- 69. Heart failure prediction Models AUC Training time / epoch Test time for 5K patients Logistic Regression 0.7900 ± 0.0111 0.15s 0.11s MLP 0.8256 ± 0.0096 0.25s 0.11s Two-layer RNN 0.8706 ± 0.0080 10.3s 0.57s RNN+attention 0.8624 ± 0.0079 6.7s 0.48s RETAIN 0.8705 ± 0.0081 10.8s 0.63s • RETAIN as accurate as RNN • Requires similar training time & test time • RETAIN is interpretable! • RNN is a blackbox 69
- 71. Conclusion • RETAIN: interpretable prediction framework • As accurate as RNN • Interpretable prediction • Predictions can be explained • Can be extended to general prognosis • What are the likely disease he/she will have in the future? • Can be used for any sequences with the two-layer structure • E.g. online shopping 71
- 73. How to generate the attentions 𝛼.? • Use another neural network model Input Layer x Hidden Layer h Output y x h = 𝝈(Wh Tx) y = wo Th (outcome −∞~ + ∞) Let’s call this function y=a(x) 73
- 74. How to generate the attentions 𝛼.? • Use function a(x) for each word: Justice, League, …, Christmas, play • Feed the scores y1, y2, …, y10 into the Softmax function League playJustice a(x1) y1 a(x2) y2 a(x10) y10 𝛼. = exp ( 𝑦.) ∑ exp ( 𝑦:)#& :;# Christmas a(x9) y9 74
- 75. How to generate the attentions 𝛼.? • Use function a(x) for each word: Justice, League, …, Christmas, play • Feed the scores y1, y2, …, y10 into the Softmax function League playJustice a(x1) y1 a(x2) y2 a(x10) y10 𝛼. = exp ( 𝑦.) ∑ exp ( 𝑦:)#& :;# Christmas a(x9) y9 Softmax function ensures 𝛼.’s sum to 1 Return75