arXiv subjects

David Sontag

Publications and source records attributed to David Sontag.

At least 91 records · Page 5Linked to original sources

arXiv2018

Optimality of Approximate Inference Algorithms on Stable Instances

Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These algorithms often find solutions that are very close to optimal. The goal of this paper is to partially explain the performance of alpha-expansion and an LP relaxation algorithm on MAP inference in Ferromagnetic Potts models (FPMs). Our main results give stability conditions under which these two algorithms provably recover the optimal MAP solution. These theoretical results complement numerous empirical observations of good performance.

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arXiv2018

Learning Weighted Representations for Generalization Across Designs

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from observational data and in unsupervised domain adaptation. We pose both of these problems as prediction under a shift in design. Popular methods for overcoming distributional shift make unrealistic assumptions such as having a well-specified model or knowing the policy that gave rise to the observed data. Other methods are hindered by their need for a pre-specified metric for comparing observations, or by poor asymptotic properties. We devise a bound on the generalization error under design shift, incorporating both representation learning and sample re-weighting. Based on the bound, we propose an algorithmic framework that does not require any of the above assumptions and which is asymptotically consistent. We empirically study the new framework using two synthetic datasets, and demonstrate its effectiveness compared to previous methods.

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arXiv2017

Causal Effect Inference with Deep Latent-Variable Models

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

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arXiv2017

Grounded Recurrent Neural Networks

In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large numbers of concepts from text. We apply the new model to address an important problem in healthcare of understanding what medical concepts are discussed in clinical text. Using a publicly available dataset derived from Intensive Care Units, we learn to label a patient's diagnoses and procedures from their discharge summary. Our evaluation shows a clear advantage to using our proposed architecture over a variety of strong baselines.

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arXiv2017

Estimating individual treatment effect: generalization bounds and algorithms

There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting individual treatment effect (ITE) from observational data, under the assumption known as strong ignorability. The algorithms learn a "balanced" representation such that the induced treated and control distributions look similar. We give a novel, simple and intuitive generalization-error bound showing that the expected ITE estimation error of a representation is bounded by a sum of the standard generalization-error of that representation and the distance between the treated and control distributions induced by the representation. We use Integral Probability Metrics to measure distances between distributions, deriving explicit bounds for the Wasserstein and Maximum Mean Discrepancy (MMD) distances. Experiments on real and simulated data show the new algorithms match or outperform the state-of-the-art.

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arXiv2017

Discourse-Based Objectives for Fast Unsupervised Sentence Representation Learning

This work presents a novel objective function for the unsupervised training of neural network sentence encoders. It exploits signals from paragraph-level discourse coherence to train these models to understand text. Our objective is purely discriminative, allowing us to train models many times faster than was possible under prior methods, and it yields models which perform well in extrinsic evaluations.

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arXiv2017

Simultaneous Learning of Trees and Representations for Extreme Classification and Density Estimation

We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of the tree, and although past work showed how to learn the tree structure, it expected that the feature vectors remained static. We provide a novel algorithm to simultaneously perform representation learning for the input data and learning of the hierarchi- cal predictor. Our approach optimizes an objec- tive function which favors balanced and easily- separable multi-way node partitions. We theoret- ically analyze this objective, showing that it gives rise to a boosting style property and a bound on classification error. We next show how to extend the algorithm to conditional density estimation. We empirically validate both variants of the al- gorithm on text classification and language mod- eling, respectively, and show that they compare favorably to common baselines in terms of accu- racy and running time.

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arXiv2016

Structured Inference Networks for Nonlinear State Space Models

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.

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arXiv2016

Recurrent Neural Networks for Multivariate Time Series with Missing Values

Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Unit (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provides useful insights for better understanding and utilization of missing values in time series analysis.

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arXiv2016

Clinical Tagging with Joint Probabilistic Models

We describe a method for parameter estimation in bipartite probabilistic graphical models for joint prediction of clinical conditions from the electronic medical record. The method does not rely on the availability of gold-standard labels, but rather uses noisy labels, called anchors, for learning. We provide a likelihood-based objective and a moments-based initialization that are effective at learning the model parameters. The learned model is evaluated in a task of assigning a heldout clinical condition to patients based on retrospective analysis of the records, and outperforms baselines which do not account for the noisiness in the labels or do not model the conditions jointly.

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arXiv2016

Multi-task Prediction of Disease Onsets from Longitudinal Lab Tests

Disparate areas of machine learning have benefited from models that can take raw data with little preprocessing as input and learn rich representations of that raw data in order to perform well on a given prediction task. We evaluate this approach in healthcare by using longitudinal measurements of lab tests, one of the more raw signals of a patient's health state widely available in clinical data, to predict disease onsets. In particular, we train a Long Short-Term Memory (LSTM) recurrent neural network and two novel convolutional neural networks for multi-task prediction of disease onset for 133 conditions based on 18 common lab tests measured over time in a cohort of 298K patients derived from 8 years of administrative claims data. We compare the neural networks to a logistic regression with several hand-engineered, clinically relevant features. We find that the representation-based learning approaches significantly outperform this baseline. We believe that our work suggests a new avenue for patient risk stratification based solely on lab results.

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arXiv2016

Identifiable Phenotyping using Constrained Non-Negative Matrix Factorization

This work proposes a new algorithm for automated and simultaneous phenotyping of multiple co-occurring medical conditions, also referred as comorbidities, using clinical notes from the electronic health records (EHRs). A basic latent factor estimation technique of non-negative matrix factorization (NMF) is augmented with domain specific constraints to obtain sparse latent factors that are anchored to a fixed set of chronic conditions. The proposed anchoring mechanism ensures a one-to-one identifiable and interpretable mapping between the latent factors and the target comorbidities. Qualitative assessment of the empirical results by clinical experts suggests that the proposed model learns clinically interpretable phenotypes while being predictive of 30 day mortality. The proposed method can be readily adapted to any non-negative EHR data across various healthcare institutions.

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arXiv2016

Train and Test Tightness of LP Relaxations in Structured Prediction

Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions required to obtain accurate predictions, both learning and inference typically require the use of approximate solvers. We propose a theoretical explanation to the striking observation that approximations based on linear programming (LP) relaxations are often tight on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that tightness generalizes from train to test data.

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arXiv2016

Temporal Convolutional Neural Networks for Diagnosis from Lab Tests

Early diagnosis of treatable diseases is essential for improving healthcare, and many diseases' onsets are predictable from annual lab tests and their temporal trends. We introduce a multi-resolution convolutional neural network for early detection of multiple diseases from irregularly measured sparse lab values. Our novel architecture takes as input both an imputed version of the data and a binary observation matrix. For imputing the temporal sparse observations, we develop a flexible, fast to train method for differentiable multivariate kernel regression. Our experiments on data from 298K individuals over 8 years, 18 common lab measurements, and 171 diseases show that the temporal signatures learned via convolution are significantly more predictive than baselines commonly used for early disease diagnosis.

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arXiv2015

Character-Aware Neural Language Models

We describe a simple neural language model that relies only on character-level inputs. Predictions are still made at the word-level. Our model employs a convolutional neural network (CNN) and a highway network over characters, whose output is given to a long short-term memory (LSTM) recurrent neural network language model (RNN-LM). On the English Penn Treebank the model is on par with the existing state-of-the-art despite having 60% fewer parameters. On languages with rich morphology (Arabic, Czech, French, German, Spanish, Russian), the model outperforms word-level/morpheme-level LSTM baselines, again with fewer parameters. The results suggest that on many languages, character inputs are sufficient for language modeling. Analysis of word representations obtained from the character composition part of the model reveals that the model is able to encode, from characters only, both semantic and orthographic information.

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arXiv2015

Barrier Frank-Wolfe for Marginal Inference

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This modular structure enables us to leverage black-box MAP solvers (both exact and approximate) for variational inference, and obtains more accurate results than tree-reweighted algorithms that optimize over the local consistency relaxation. Theoretically, we bound the sub-optimality for the proposed algorithm despite the TRW objective having unbounded gradients at the boundary of the marginal polytope. Empirically, we demonstrate the increased quality of results found by tightening the relaxation over the marginal polytope as well as the spanning tree polytope on synthetic and real-world instances.

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arXiv2015

Deep Kalman Filters

Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent variational methods for learning deep generative models, we introduce a unified algorithm to efficiently learn a broad spectrum of Kalman filters. Of particular interest is the use of temporal generative models for counterfactual inference. We investigate the efficacy of such models for counterfactual inference, and to that end we introduce the "Healing MNIST" dataset where long-term structure, noise and actions are applied to sequences of digits. We show the efficacy of our method for modeling this dataset. We further show how our model can be used for counterfactual inference for patients, based on electronic health record data of 8,000 patients over 4.5 years.

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arXiv2015

Anchored Discrete Factor Analysis

We present a semi-supervised learning algorithm for learning discrete factor analysis models with arbitrary structure on the latent variables. Our algorithm assumes that every latent variable has an "anchor", an observed variable with only that latent variable as its parent. Given such anchors, we show that it is possible to consistently recover moments of the latent variables and use these moments to learn complete models. We also introduce a new technique for improving the robustness of method-of-moment algorithms by optimizing over the marginal polytope or its relaxations. We evaluate our algorithm using two real-world tasks, tag prediction on questions from the Stack Overflow website and medical diagnosis in an emergency department.

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