In order to construct accurate proposers for Metropolis-Hastings Markov Chain Monte Carlo, we integrate ideas from probabilistic graphical models and neural networks in an open-source framework we call Lightweight Inference Compilation (LIC). LIC implements amortized inference within an open-universe declarative probabilistic programming language (PPL). Graph neural networks are used to parameterize proposal distributions as functions of Markov blankets, which during "compilation" are optimized to approximate single-site Gibbs sampling distributions. Unlike prior work in inference compilation (IC), LIC forgoes importance sampling of linear execution traces in favor of operating directly on Bayesian networks. Through using a declarative PPL, the Markov blankets of nodes (which may be non-static) are queried at inference-time to produce proposers Experimental results show LIC can produce proposers which have less parameters, greater robustness to nuisance random variables, and improved posterior sampling in a Bayesian logistic regression and $n$-schools inference application.

Recommending the best course of action for an individual is a major application of individual-level causal effect estimation. This application is often needed in safety-critical domains such as healthcare, where estimating and communicating uncertainty to decision-makers is crucial. We introduce a practical approach for integrating uncertainty estimation into a class of state-of-the-art neural network methods used for individual-level causal estimates. We show that our methods enable us to deal gracefully with situations of "no-overlap", common in high-dimensional data, where standard applications of causal effect approaches fail. Further, our methods allow us to handle covariate shift, where test distribution differs to train distribution, common when systems are deployed in practice. We show that when such a covariate shift occurs, correctly modeling uncertainty can keep us from giving overconfident and potentially harmful recommendations. We demonstrate our methodology with a range of state-of-the-art models. Under both covariate shift and lack of overlap, our uncertainty-equipped methods can alert decisions makers when predictions are not to be trusted while outperforming their uncertainty-oblivious counterparts.

Should sequences be modeled autoregressively---one symbol at a time? How much computation is needed to predict the next symbol? While local normalization is cheap, this also limits its power. We point out that some probability distributions over discrete sequences cannot be well-approximated by any autoregressive model whose runtime and parameter size grow polynomially in the sequence length---even though their unnormalized sequence probabilities are efficient to compute exactly. Intuitively, the probability of the next symbol can be expensive to compute or approximate (even via randomized algorithms) when it marginalizes over exponentially many possible futures, which is in general $\mathrm{NP}$-hard. Our result is conditional on the widely believed hypothesis that $\mathrm{NP} \nsubseteq \mathrm{P/poly}$ (without which the polynomial hierarchy would collapse at the second level). This theoretical observation serves as a caution to the viewpoint that pumping up parameter size is a straightforward way to improve autoregressive models (e.g., in language modeling). It also suggests that globally normalized (energy-based) models may sometimes outperform locally normalized (autoregressive) models, as we demonstrate experimentally for language modeling.

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and can use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers can only sample from posterior densities that are differentiable almost everywhere, which precludes their use for model choice. Motivated by variable selection problems, we show how to develop reversible jump PDMP samplers that can jointly explore the discrete space of models and the continuous space of parameters. Our framework is general: it takes any existing PDMP sampler, and adds two types of trans-dimensional moves that allow for the addition or removal of a variable from the model. We show how the rates of these trans-dimensional moves can be calculated so that the sampler has the correct invariant distribution. Simulations show that the new samplers can mix better than standard MCMC algorithms. Our empirical results show they are also more efficient than gradient-based samplers that avoid model choice through use of continuous spike-and-slab priors which replace a point mass at zero for each parameter with a density concentrated around zero.

Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regression. We provide non-asymptotic theoretical guarantees for the VB posterior in both $\ell_2$ and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. This framework leads to bounds that depend on the conditional information density between the the output hypothesis and the choice of the training set, given a larger set of data samples from which the training set is formed. If the conditional information density is bounded uniformly in the sizenof the training set, our bounds decay as1/n, which is referred to as a fast rate. This is in contrast with the tail bounds involving conditional information measures available in the literature, which have a less benign 1/ n dependence. We demonstrate the usefulness of our tail bounds by showing that they lead to estimates of the test loss achievable with several neural network architectures trained on MNIST and Fashion-MNIST that match the state-of-the-art bounds available in the literature. In recent years, there has been a surge of interest in the use of information-theoretic techniques for bounding the loss of learning algorithms. While the first results of this flavor can be traced to the probably approximately correct (PAC)-Bayesian approach (McAllester, 1998; Catoni, 2007) (see also (Guedj, 2019) for a recent review), the connection between loss bounds and classical information-theoretic measures was made explicit in the works of Russo & Zou (2016) and Xu & Raginsky (2017), where bounds on the average population loss were derived in terms of the mutual information between the training data and the output hypothesis. Since then, these average loss bounds have been tightened (Bu et al., 2019; Asadi et al., 2018; Negrea et al., 2019). Furthermore, the information-theoretic framework has also been successfully applied to derive tail probability bounds on the population loss (Bassily et al., 2018; Esposito et al., 2019; Hellström & Durisi, 2020a). Of particular relevance to the present paper is the random-subset setting, introduced by Steinke & Zakynthinou (2020) and further studied in (Hellström & Durisi, 2020b; Haghifam et al., 2020).

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC is sensitive to outliers, which is caused by an inappropriate choice of the data discrepancy measure. In this paper, we propose to use a nearest-neighbor-based $\gamma$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear time complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

We present two methods to reduce the complexity of Bayesian network (BN) classifiers. First, we introduce quantization-aware training using the straight-through gradient estimator to quantize the parameters of BNs to few bits. Second, we extend a recently proposed differentiable tree-augmented naive Bayes (TAN) structure learning approach by also considering the model size. Both methods are motivated by recent developments in the deep learning community, and they provide effective means to trade off between model size and prediction accuracy, which is demonstrated in extensive experiments. Furthermore, we contrast quantized BN classifiers with quantized deep neural networks (DNNs) for small-scale scenarios which have hardly been investigated in the literature. We show Pareto optimal models with respect to model size, number of operations, and test error and find that both model classes are viable options.

Discrete latent spaces in variational autoencoders have been shown to effectively capture the data distribution for many real-world problems such as natural language understanding, human intent prediction, and visual scene representation. However, discrete latent spaces need to be sufficiently large to capture the complexities of real-world data, rendering downstream tasks computationally challenging. For instance, performing motion planning in a high-dimensional latent representation of the environment could be intractable. We consider the problem of sparsifying the discrete latent space of a trained conditional variational autoencoder, while preserving its learned multimodality. As a post hoc latent space reduction technique, we use evidential theory to identify the latent classes that receive direct evidence from a particular input condition and filter out those that do not. Experiments on diverse tasks, such as image generation and human behavior prediction, demonstrate the effectiveness of our proposed technique at reducing the discrete latent sample space size of a model while maintaining its learned multimodality.