Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior collapse as a problem of latent variable non-identifiability. We prove that the posterior collapses if and only if the latent variables are non-identifiable in the generative model. This fact implies that posterior collapse is not a phenomenon specific to the use of flexible distributions or approximate inference. Rather, it can occur in classical probabilistic models even with exact inference, which we also demonstrate. Based on these results, we propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. This model class resolves the problem of latent variable non-identifiability by leveraging bijective Brenier maps and parameterizing them with input convex neural networks, without special variational inference objectives or optimization tricks. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.
Fairness in clinical decision-making is a critical element of health equity, but assessing fairness of clinical decisions from observational data is challenging. Recently, many fairness notions have been proposed to quantify fairness in decision-making, among which causality-based fairness notions have gained increasing attention due to its potential in adjusting for confounding and reasoning about bias. However, causal fairness notions remain under-explored in the context of clinical decision-making with large-scale healthcare data. In this work, we propose a Bayesian causal inference approach for assessing a causal fairness notion called principal fairness in clinical settings. We demonstrate our approach using both simulated data and electronic health records (EHR) data.
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from an estimated generative model. It is efficient and compatible with either explicit or implicit conditional generative models. Theoretically, we show that PCP guarantees correct marginal coverage with finite samples. Empirically, we study PCP on a variety of simulated and real datasets. Compared to existing methods for conformal inference, PCP provides sharper predictive sets.
Understanding career trajectories -- the sequences of jobs that individuals hold over their working lives -- is important to economists for studying labor markets. In the past, economists have estimated relevant quantities by fitting predictive models to small surveys, but in recent years large datasets of online resumes have also become available. These new datasets provide job sequences of many more individuals, but they are too large and complex for standard econometric modeling. To this end, we adapt ideas from modern language modeling to the analysis of large-scale job sequence data. We develop CAREER, a transformer-based model that learns a low-dimensional representation of an individual's job history. This representation can be used to predict jobs directly on a large dataset, or can be "transferred" to represent jobs in smaller and better-curated datasets. We fit the model to a large dataset of resumes, 24 million people who are involved in more than a thousand unique occupations. It forms accurate predictions on held-out data, and it learns useful career representations that can be fine-tuned to make accurate predictions on common economics datasets.
Variational inference often minimizes the "reverse" Kullbeck-Leibler (KL) KL(q||p) from the approximate distribution q to the posterior p. Recent work studies the "forward" KL KL(p||q), which unlike reverse KL does not lead to variational approximations that underestimate uncertainty. This paper introduces Transport Score Climbing (TSC), a method that optimizes KL(p||q) by using Hamiltonian Monte Carlo (HMC) and a novel adaptive transport map. The transport map improves the trajectory of HMC by acting as a change of variable between the latent variable space and a warped space. TSC uses HMC samples to dynamically train the transport map while optimizing KL(p||q). TSC leverages synergies, where better transport maps lead to better HMC sampling, which then leads to better transport maps. We demonstrate TSC on synthetic and real data. We find that TSC achieves competitive performance when training variational autoencoders on large-scale data.
We present neural activation coding (NAC) as a novel approach for learning deep representations from unlabeled data for downstream applications. We argue that the deep encoder should maximize its nonlinear expressivity on the data for downstream predictors to take full advantage of its representation power. To this end, NAC maximizes the mutual information between activation patterns of the encoder and the data over a noisy communication channel. We show that learning for a noise-robust activation code increases the number of distinct linear regions of ReLU encoders, hence the maximum nonlinear expressivity. More interestingly, NAC learns both continuous and discrete representations of data, which we respectively evaluate on two downstream tasks: (i) linear classification on CIFAR-10 and ImageNet-1K and (ii) nearest neighbor retrieval on CIFAR-10 and FLICKR-25K. Empirical results show that NAC attains better or comparable performance on both tasks over recent baselines including SimCLR and DistillHash. In addition, NAC pretraining provides significant benefits to the training of deep generative models. Our code is available at https://github.com/yookoon/nac.
We develop the Sparse VAE, a deep generative model for unsupervised representation learning on high-dimensional data. Given a dataset of observations, the Sparse VAE learns a set of latent factors that captures its distribution. The model is sparse in the sense that each feature of the dataset (i.e., each dimension) depends on a small subset of the latent factors. As examples, in ratings data each movie is only described by a few genres; in text data each word is only applicable to a few topics; in genomics, each gene is active in only a few biological processes. We first show that the Sparse VAE is identifiable: given data drawn from the model, there exists a uniquely optimal set of factors. (In contrast, most VAE-based models are not identifiable.) The key assumption behind Sparse-VAE identifiability is the existence of "anchor features", where for each factor there exists a feature that depends only on that factor. Importantly, the anchor features do not need to be known in advance. We then show how to fit the Sparse VAE with variational EM. Finally, we empirically study the Sparse VAE with both simulated and real data. We find that it recovers meaningful latent factors and has smaller heldout reconstruction error than related methods.
This paper presents a new optimization approach to causal estimation. Given data that contains covariates and an outcome, which covariates are causes of the outcome, and what is the strength of the causality? In classical machine learning (ML), the goal of optimization is to maximize predictive accuracy. However, some covariates might exhibit a non-causal association to the outcome. Such spurious associations provide predictive power for classical ML, but they prevent us from causally interpreting the result. This paper proposes CoCo, an optimization algorithm that bridges the gap between pure prediction and causal inference. CoCo leverages the recently-proposed idea of environments, datasets of covariates/response where the causal relationships remain invariant but where the distribution of the covariates changes from environment to environment. Given datasets from multiple environments -- and ones that exhibit sufficient heterogeneity -- CoCo maximizes an objective for which the only solution is the causal solution. We describe the theoretical foundations of this approach and demonstrate its effectiveness on simulated and real datasets. Compared to classical ML and existing methods, CoCo provides more accurate estimates of the causal model.
Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find sequential rationales by solving a combinatorial optimization: the best rationale is the smallest subset of input tokens that would predict the same output as the full sequence. Enumerating all subsets is intractable, so we propose an efficient greedy algorithm to approximate this objective. The algorithm, which is called greedy rationalization, applies to any model. For this approach to be effective, the model should form compatible conditional distributions when making predictions on incomplete subsets of the context. This condition can be enforced with a short fine-tuning step. We study greedy rationalization on language modeling and machine translation. Compared to existing baselines, greedy rationalization is best at optimizing the combinatorial objective and provides the most faithful rationales. On a new dataset of annotated sequential rationales, greedy rationales are most similar to human rationales.