Causal Phenotype Discovery via Deep Networks Dave Kale 1 , 2 , - - PowerPoint PPT Presentation

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Causal Phenotype Discovery via Deep Networks Dave Kale 1 , 2 , - - PowerPoint PPT Presentation

Causal Phenotype Discovery via Deep Networks Dave Kale 1 , 2 , Zhengping Che 1 M. Taha Bahadori 1 , Wenzhe Li 1 , Yan Liu 1 Randall Wetzel 2 1 University of Southern California, Computer Science 2 Laura P. and Leland K. Whittier VPICU, Childrens


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Causal Phenotype Discovery via Deep Networks

Dave Kale1,2, Zhengping Che1

  • M. Taha Bahadori1, Wenzhe Li1, Yan Liu1

Randall Wetzel2

1 University of Southern California, Computer Science 2 Laura P. and Leland K. Whittier VPICU, Children’s Hospital LA

November 20, 2015

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 1 / 27

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Disclosures and Funding

Disclosures

  • D. Kale, Z. Che, T. Bahadori, W. Li, and Y. Liu have no commercial
  • r financial interests related to this work.
  • R. Wetzel is CEO of Virtual PICU (VPS) Systems, LLC.

Funding

  • D. Kale is funded by a Innovation in Engineering Fellowship from the

Alfred E. Mann Institute at USC.

  • The VPICU is funded by a grant from the Laura P. and Leland K.

Whittier Foundation.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 2 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 3 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 4 / 27

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Electronic (or computational) phenotyping

Rules/algorithms that define diagnostic/inclusion criteria [PheKB].

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 5 / 27

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Electronic (or computational) phenotyping

Rules/algorithms that define diagnostic/inclusion criteria [PheKB]. Classifiers that answer the question “does patient have X?” [AL14] [AP14]

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 5 / 27

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Electronic (or computational) phenotyping

Rules/algorithms that define diagnostic/inclusion criteria [PheKB]. Classifiers that answer the question “does patient have X?” [AL14] [AP14] Clusters of patients with similar symptoms/signs [MK12] [SWS15].

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 5 / 27

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Electronic (or computational) phenotyping

Rules/algorithms that define diagnostic/inclusion criteria [PheKB]. Classifiers that answer the question “does patient have X?” [AL14] [AP14] Clusters of patients with similar symptoms/signs [MK12] [SWS15]. Latent factors/bases for diagnoses, procedures, etc. [HGS14] [ZW14].

Phenotype R! Procedures factor! Diagnosis factor! Patients 
 factor! Phenotype importance! Phenotype 1! Patients! Procedures! Diagnoses!

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 5 / 27

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Computational phenotyping of critical illness

Our setting: learning critical illness phenotypes from multivariate PICU time series.

20 30 40 50 60 70 80 DBP 40 50 60 70 80 90 100 110 120 SBP 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 CRR 15 20 25 30 35 40 ETCO2 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 FIO2 2 4 6 8 10 12 14 16 TGCS 100 120 140 160 180 200 220 240 Gluc 2 4 6 8 10 12 14 60 80 100 120 140 160 180 200 HR 2 4 6 8 10 12 14 7.10 7.15 7.20 7.25 7.30 7.35 7.40 pH 2 4 6 8 10 12 14 10 15 20 25 30 35 40 45 RR 2 4 6 8 10 12 14 75 80 85 90 95 100 SAO2 2 4 6 8 10 12 14 31 32 33 34 35 36 37 38 T emp 2 4 6 8 10 12 0.0 0.5 1.0 1.5 2.0 2.5 UO 2 4 6 8 10 12 0.0 0.2 0.4 0.6 0.8 1.0

Deformable motifs [SDK11] Bayesian clustering [MK12] Multi-task GPs [GP15] Subspace clustering [BK15]

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 6 / 27

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Phenotyping as representation learning

Medicine: phenotypes, biomarkers [BD01]

1 Measurable attributes of patient/disease. 2 Independent of other biomarkers. 3 Separate patients into meaningful groups. 4 Improve outcome prediction, risk assessment. 5 Clinically plausible, interpretable.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 7 / 27

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Phenotyping as representation learning

Medicine: phenotypes, biomarkers [BD01]

1 Measurable attributes of patient/disease. 2 Independent of other biomarkers. 3 Separate patients into meaningful groups. 4 Improve outcome prediction, risk assessment. 5 Clinically plausible, interpretable.

Machine learning: features, representations [BCV13]

1 Measurable properties of objects. 2 Independent, disentangle factors of variation. 3 Form natural clusters. 4 Useful for discriminative, predictive tasks. 5 Interpretable, provide insight into problem.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 7 / 27

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Deep learning of representations

Representation learning: learn transformation of data useful for some task.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 8 / 27

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Deep learning of representations

Representation learning: learn transformation of data useful for some task. Main tool: neural networks (feedforward nets, ConvNets, RNNs, etc.)

  • Date back to 40s; abandoned in 90s.
  • Revived as deep learning in 2000s.

(new methods, big data, faster hardware)

  • State-of-the-art in vision, speech, NLP
  • Google, Apple, Microsoft, Facebook
  • Biologically inspired (if not plausible).
  • Maximally varying, nonlinear functions.
  • Exploit labeled and unlabeled data.
  • Layers yield increasing abstraction.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 8 / 27

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Deep learning of representations

Representation learning: learn transformation of data useful for some task. Main tool: neural networks (feedforward nets, ConvNets, RNNs, etc.) Output: ˆ y = g(hLWout + bout)

  • sigmoid for binary classification
  • softmax for multiclass classification
  • identity for regression

Hidden: ˆ hℓ = h(hℓ−1Wℓ + bℓ)

  • sigmoid or tanh traditional
  • rectified linear (h(a) = max(0, a)) popular

Input: ˆ h0 = x

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 8 / 27

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Deep learning of representations

Representation learning: learn transformation of data useful for some task. Main tool: neural networks (feedforward nets, ConvNets, RNNs, etc.)

Train using gradient descent.

Cost: C(y, x; {Wℓ, bℓ}) (denote C) Update: Wℓ(i, j) = Wℓ(i, j) − α

∂C ∂Wℓ(i,j)

Computing the gradients via backpropagation:

∂C ∂Wℓ(i,j) = ∂C ∂hℓ(j) ∂hℓ(j) ∂aℓ(j) ∂aℓ(j) ∂Wℓ(i,j) where ∂hℓ(j) ∂aℓ(j) = g′(aℓ(j)) ∂aℓ(j) ∂Wℓ(i,j) = hℓ−1(i) ∂C ∂hℓ(j) = k Wℓ+1(j, k) ∂C hℓ+1(k)

aℓ(j) = hℓ−1Wℓ(:, j) + bj

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 8 / 27

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Neural nets combine different views of CP

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Neural nets combine different views of CP

Output layer: classifier

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 9 / 27

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Neural nets combine different views of CP

Output layer: classifier Hidden layers:

Latent factors/bases

0.97 ¡ 0.11 ¡ 0.43 ¡ 0.88 ¡ 0.67 ¡ 0.52 ¡ 0.18 ¡ 0.92 ¡ 0.89 ¡ 0.08 ¡

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 9 / 27

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Neural nets combine different views of CP

Output layer: classifier Hidden layers:

Latent factors/bases Multiclustering [BC13]

0.97 ¡ 0.11 ¡ 0.43 ¡ 0.88 ¡ 0.67 ¡ 0.52 ¡ 0.18 ¡ 0.92 ¡ 0.89 ¡ 0.08 ¡

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 9 / 27

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Major challenge of neural nets: interpretation

No predefined semantics (vs. graphical model) Learned bases not guaranteed to be uncorrelated or independent (vs. PCA, ICA) Information contained in distributed activations, so interpreting individual features unreliable [SZ14]

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 10 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 11 / 27

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Deep learning for time series: window-based approach

Classifica(on Feature extrac(on

h(l) ŷ

  • Apply neural net (NNet) to fixed-size

windows (subsequences).

  • Classification, feature extraction.
  • Correlations across variables, time.
  • Relatively few, weak model assumptions.
  • Can learn to detect smooth,

trajectory-like patterns.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 12 / 27

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Deep learning for time series: window-based approach

Can also be applied in sliding window fashion to longer time series.

Classifica(on Feature extrac(on ht1 ŷt1 ht2 ŷt2 ht3 ŷt3 X[t1:t1+T] ˆ y = maxy 1 N P(y | Xt)

t

Full Time Series Classifica(on X[t2:t2+T] X[t3:t3+T]

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 13 / 27

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Causal analysis of learned phenotypic features

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

  • Analyze of causal relationship between each factor, response.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

  • Analyze of causal relationship between each factor, response.
  • Choose causal direction of each edge: hi → y or hi ← y.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

  • Analyze of causal relationship between each factor, response.
  • Choose causal direction of each edge: hi → y or hi ← y.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

  • Analyze of causal relationship between each factor, response.
  • Choose causal direction of each edge: hi → y or hi ← y.
  • Use only causal factors (hi → y) in further analysis.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis of learned phenotypic features

  • Now have set of D latent factors {hi}D

i=1, response y.

  • Analyze of causal relationship between each factor, response.
  • Choose causal direction of each edge: hi → y or hi ← y.
  • Use only causal factors (hi → y) in further analysis.
  • Note: for predictive tasks, use original network.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 14 / 27

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Causal analysis with pairwise likelihood ratios [HS13]

For two variables h and y, want to distinguish between two causal models: h → y : y = ρh + d h ← y : h = ρy + e h, y are non-Gaussian. Noise d (e) is independent of x (y). Model log-likelihood: log L(h → y) = log ph(h) + log pd

  • y−ρh

1−ρ2

  • − log(1 − ρ2).

Sign of likelihood ratio determines direction of causal edge: R = log L(h → y) − log L(h ← y) R > 0 if h → y R < 0 if h ← y Important note: makes no statement about strength of edge. Use in combination with feature selection!

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 15 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 16 / 27

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Clinical data sets

8500 multivariate time series from CHLA PICU (PICU) [7]:

  • All > 24 hours long.
  • Sampled once per hour (after preprocessing∗).
  • 13 variables: vitals, labs, outputs, assessments.
  • Phenotype labels: 67 groups of ICD-9 codes, 19 standard ICD-9

categories.

∗ Age correction (PICU only), resampling, imputation, rescaling, etc. Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 17 / 27

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Clinical data sets

8500 multivariate time series from CHLA PICU (PICU) [7]:

  • All > 24 hours long.
  • Sampled once per hour (after preprocessing∗).
  • 13 variables: vitals, labs, outputs, assessments.
  • Phenotype labels: 67 groups of ICD-9 codes, 19 standard ICD-9

categories. 8000 multivariate time series from PhysioNet Challenge 2012 † (PC2012):

  • 48 hours long (not full episodes in all cases).
  • Sampled once per hour (after preprocessing∗).
  • 33 variables: vitals, labs, outputs, assessments.
  • Label: in-hospital mortality

∗ Age correction (PICU only), resampling, imputation, rescaling, etc. † http://physionet.org/challenge/2012/ Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 17 / 27

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General experimental setup

1 Data preparation

  • Generate 5-10 random training/validation/test splits of episodes.
  • Train on fixed-size windows of time series:
  • PC2012: full 48 hour time series.
  • PICU: 12 hour windows extracted in sliding window fashion.

2 Model architecture, training details

  • 3 hidden layers, fully connected, sigmoid activation.
  • Unsupervised pretraining with stochastic denoising autoencoders.
  • Supervised training (with early stopping) as multilayer perceptron.

3 Evaluation

  • Quantitative: area under ROC curve (AUROC), area under

precision-recall curve (AUPRC), precision at 90% recall.

  • Qualitative: causal feature analysis + visualization.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 18 / 27

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First 48-hour mortality prediction (PC2012)

AUROC AUPRC Prec@90%Rec Raw (R) 0.787 ± 0.0290 0.407 ± 0.0429 0.221 ± 0.0171 HandDesigned (H) 0.829 ± 0.0211 0.468 ± 0.0479 0.259 ± 0.0494 NNet(R,3) 0.821 ± 0.0210 0.444 ± 0.0324 0.256 ± 0.0303 NNet(H,3) 0.832 ± 0.0162 0.462 ± 0.0480 0.271 ± 0.0260 H+R 0.823 ± 0.0183 0.438 ± 0.0354 0.256 ± 0.0319 H+NNet(R,3) 0.845 ± 0.0165 0.487 ± 0.0473 0.291 ± 0.0335

Mean performance with standard deviation (10 folds); classifier: linear SVM + L1 penalty.

NeuralNet: Layer 3 hidden unit activations of neural net (3 layer neural net, unsupervised + supervised training) HandDesigned: extremes, central tendencies, variance, trends

PICU classification results: Che, Kale, Li, Bahadori, and Liu, SIGKDD 2015 [CK15]

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 19 / 27

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Phenotype for septic shock (ICD-9: 990-995)

  • Very irregular physiology, known symptoms of sepsis.
  • Low Glascow coma score indicates patient is unconscious.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 20 / 27

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Phenotype for circulatory disease (ICD-9: 390-459)

  • Elevated blood pressure and heart rate, depressed pH.
  • Evidence of ventilation (elevated FIO2).
  • Note elevated urine output; also correlated with urinary disorders.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 21 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 22 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Related: Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational

  • Phenotyping. SIGKDD 2015.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Related: Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational

  • Phenotyping. SIGKDD 2015.

Future work:

  • Think deeply about what we mean by causality in this setting.
  • Further empirical investigation of learned representations.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Related: Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational

  • Phenotyping. SIGKDD 2015.

Future work:

  • Think deeply about what we mean by causality in this setting.
  • Further empirical investigation of learned representations.
  • Combine causal analysis, representation learning. See [CP15] for example.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Related: Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational

  • Phenotyping. SIGKDD 2015.

Future work:

  • Think deeply about what we mean by causality in this setting.
  • Further empirical investigation of learned representations.
  • Combine causal analysis, representation learning. See [CP15] for example.
  • Take into account temporality, treatment effects.

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Conclusion

We have presented

  • a conceptual framework for discovery of causal phenotypic representations.
  • empirical results showing it can discover relevant phenotypes.

Related: Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational

  • Phenotyping. SIGKDD 2015.

Future work:

  • Think deeply about what we mean by causality in this setting.
  • Further empirical investigation of learned representations.
  • Combine causal analysis, representation learning. See [CP15] for example.
  • Take into account temporality, treatment effects.

Dave Kale: http://www-scf.usc.edu/~dkale/ Zhengping Che: http://www-scf.usc.edu/~zche/ Yan Liu: http://www-bcf.usc.edu/~liu32/

Thank you and fight on!

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 23 / 27

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Outline

1 Background: why and how of computational phenotyping

Phenotypes: representations of illness Computational phenotyping Phenotyping as representation learning

2 Phenotyping clinical time series with deep learning

Deep learning for time series Causal analysis of phenotypic representations

3 Experiments

Setup Prediction results Visualization of causal phenotypes

4 Conclusion 5 References

Kale/Che (USC/VPICU) Learning Causal Phenotypes November 20, 2015 24 / 27

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References I

[CK15] Z. Che, D. Kale, W. Li, T. Bahadori, Y. Liu. Deep Computational Phenotyping. SIGKDD 2015. [OC15] A. Oellrich∗, N. Collier∗, T. Groza∗, D. Rebholz-Schuhmann∗, N.H. Shah∗, et al. The digital revolution in phenotyping. Briefings in Bioinformatics, 2015: 112. [W15] A.B. Wilcox. Leveraging Electronic Health Records for Phenotyping. Translational Informatics: Realizing the Promise of Knowledge-Driven Healthcare (Health Informatics). P.R.O. Payne and P.J. Embi (eds.). Springer-Verlag, London, 2015, pg. 61-74. [PheKB] Phenotyping KnowledgeBase project: https://phekb.org/ [MK12] B. Marlin, D. Kale, R. Khemani, and R. Wetzel. Unsupervised Pattern Discovery in Electronic Health Care Data Using Probabilistic Clustering Models. IHI 2012. [LDL13] T.A. Lasko, J.C. Denny, and M.A. Levy. Computational Phenotype Discovery Using Unsupervised Feature Learning over Noisy, Sparse, and Irregular Clinical Data. PLoS ONE 8 (6): e66341, 2013. [PheKB] TODO. [AL14] V. Agarwal and N.H. Shah, et al. Using narratives as a source to automatically learn phenotype models. AMIA DMMI Workshop 2014. [AP15] V. Agarwal and N.H. Shah, et al. Learning statistical models of phenotypes using noisy labeled training data. Under review.

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References II

[SWS15] P. Schulam, F. Wigley, and S. Saria. Clustering Longitudinal Clinical Marker Trajectories from Electronic Health Data: Applications to Phenotyping and Endotype

  • Discovery. AAAI 2015.

[HGS14] J. Ho, J. Ghosh, and J. Sun. Marble: high-throughput phenotyping from electronic health records via sparse nonnegative tensor factorization. ACM SIGKDD 2014. [ZW14] J. Zhou, F. Wang, J. Hu, and J. Ye. From micro to macro: Data driven phenotyping by densification of longitudinal electronic medical records. ACM SIGKDD 2014. [SDK11] S. Saria, A. Duchi, and D. Koller. Discovering deformable motifs in continuous time series data. IJCAI 2011. [GP15] M. Ghassemi∗, M. Pimentel∗, T. Naumann, T. Brennan, D. Clifton, P. Szolovits, and M. Feng. A Multivariate Timeseries Modeling Approach to Severity of Illness Assessment and Forecasting in ICU with Sparse, Heterogeneous Clinical Data. AAAI 2015. [BK15] T. Bahadori, D. Kale, Y. Fan, and Y. Liu. Functional Subspace Clustering with Application to Time Series. ICML 2015.

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References III

[BD01] Biomarkers Definitions Working Group. Biomarkers and surrogate endpoints: preferred definitions and conceptual framework. Clin Pharmacol Ther, 69 (3): 89-95, Mar 2001. [BCV13] Y. Bengio, A. Courville, and P. Vincent. Representation Learning: A Review and New Perspectives. TPAMI 2013. [SZ14] C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R.

  • Fergus. Intriguing properties of neural networks. ICLR 2014.

[HS13] A. Hyv¨ arinen and S. Smith. Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. JMLR 2013. [CP15] F. Chalupka, P. Perona, and F. Eberhardt. Visual Causal Feature Learning. UAI 2015.

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