It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

The task of drawing samples efficiently from high-dimensional complex probability distributions enables us to perform inference using complex statistical models from large amounts of data, where uncertainty quantification is of paramount importance to understand the intrinsic risk associated with every decision made with models learned from data. The ability to quantify uncertainty when comparing a theoretical or computational model to observations is critical to conducting a sound scientific investigation, particularly in machine-learned models and in the physical sciences like physics [92]. More specifically, Bayesian inference [96, 184] is a prominent method for linking models and observations and estimating uncertainties, in which sampling techniques are widely adopted, which also finds applications to various areas such as imaging processing and inverse problems (see e.g., [87]), and Bayesian neural networks and deep learning [134], etc. While Markov chain Monte Carlo (MCMC) methods [164] have been the major workhorse of such sampling tasks, most traditional MCMC algorithms were regarded as unscalable to high dimensions. In particular, in modern large-scale applications such as Bayesian deep learning in the overparameterized regime in which we want to make posterior inference on the neural network weights, traditional MCMC algorithms become computationally prohibitive in such high dimensions and alternative approaches such as variational inference (VI; see e.g., [21]) have been widely adopted.

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work is to investigate how far this interpretation can be realized by current sequence prediction models and training regimes. The focus is on piecewise stationary sources with unobserved switching-points, which arguably capture an important characteristic of natural language and action-observation sequences in partially observable environments. We show that various types of memory-based neural models, including Transformers, LSTMs, and RNNs can learn to accurately approximate known Bayes-optimal algorithms and behave as if performing Bayesian inference over the latent switching-points and the latent parameters governing the data distribution within each segment.

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. Our monitors are of two types, and use, respectively, frequentist and Bayesian statistical inference techniques. While the frequentist monitors compute estimates that are objectively correct with respect to the ground truth, the Bayesian monitors compute estimates that are correct subject to a given prior belief about the system's model. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. Although they exhibit different theoretical complexities in certain cases, in our experiments, both frequentist and Bayesian monitors took less than a millisecond to update their verdicts after each observation.

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that they are restricted to discrete spaces. We present a theory for generalized GFlowNets, which encompasses both existing discrete GFlowNets and ones with continuous or hybrid state spaces, and perform experiments with two goals in mind. First, we illustrate critical points of the theory and the importance of various assumptions. Second, we empirically demonstrate how observations about discrete GFlowNets transfer to the continuous case and show strong results compared to non-GFlowNet baselines on several previously studied tasks. This work greatly widens the perspectives for the application of GFlowNets in probabilistic inference and various modeling settings.

Randomized controlled trials (RCTs) are considered the gold standard for estimating the average treatment effect (ATE) of interventions. One use of RCTs is to study the causes of global poverty -- a subject explicitly cited in the 2019 Nobel Memorial Prize awarded to Duflo, Banerjee, and Kremer "for their experimental approach to alleviating global poverty." Because the ATE is a population summary, anti-poverty experiments often seek to unpack the effect variation around the ATE by conditioning (CATE) on tabular variables such as age and ethnicity that were measured during the RCT data collection. Although such variables are key to unpacking CATE, using only such variables may fail to capture historical, geographical, or neighborhood-specific contributors to effect variation, as tabular RCT data are often only observed near the time of the experiment. In global poverty research, when the location of the experiment units is approximately known, satellite imagery can provide a window into such factors important for understanding heterogeneity. However, there is no method that specifically enables applied researchers to analyze CATE from images. In this paper, using a deep probabilistic modeling framework, we develop such a method that estimates latent clusters of images by identifying images with similar treatment effects distributions. Our interpretable image CATE model also includes a sensitivity factor that quantifies the importance of image segments contributing to the effect cluster prediction. We compare the proposed methods against alternatives in simulation; also, we show how the model works in an actual RCT, estimating the effects of an anti-poverty intervention in northern Uganda and obtaining a posterior predictive distribution over effects for the rest of the country where no experimental data was collected. We make all models available in open-source software.

Navigating to destinations using human speech instructions is essential for autonomous mobile robots operating in the real world. Although robots can take different paths toward the same goal, the shortest path is not always optimal. A desired approach is to flexibly accommodate waypoint specifications, planning a better alternative path, even with detours. Furthermore, robots require real-time inference capabilities. Spatial representations include semantic, topological, and metric levels, each capturing different aspects of the environment. This study aims to realize a hierarchical spatial representation by a topometric semantic map and path planning with speech instructions, including waypoints. We propose SpCoTMHP, a hierarchical path-planning method that utilizes multimodal spatial concepts, incorporating place connectivity. This approach provides a novel integrated probabilistic generative model and fast approximate inference, with interaction among the hierarchy levels. A formulation based on control as probabilistic inference theoretically supports the proposed path planning. Navigation experiments using speech instruction with a waypoint demonstrated the performance improvement of path planning, WN-SPL by 0.589, and reduced computation time by 7.14 sec compared to conventional methods. Hierarchical spatial representations offer a mutually understandable form for humans and robots, enabling language-based navigation tasks.

In high-dimensional Bayesian statistics, several methods have been developed, including many prior distributions that lead to the sparsity of estimated parameters. However, such priors have limitations in handling the spectral eigenvector structure of data, and as a result, they are ill-suited for analyzing over-parameterized models (high-dimensional linear models that do not assume sparsity) that have been developed in recent years. This paper introduces a Bayesian approach that uses a prior dependent on the eigenvectors of data covariance matrices, but does not induce the sparsity of parameters. We also provide contraction rates of derived posterior distributions and develop a truncated Gaussian approximation of the posterior distribution. The former demonstrates the efficiency of posterior estimation, while the latter enables quantification of parameter uncertainty using a Bernstein-von Mises-type approach. These results indicate that any Bayesian method that can handle the spectrum of data and estimate non-sparse high dimensions would be possible.

Neal in his seminal work [1] pointed out that a shallow but infinitely wide random neural network is a Gaussian process (GP) [2] in statistical sense. Subsequent work [3, 4] in interpreting neural network with specific nonlinear activation units as kernel machines was also inspired by such idea. More recent reports [5, 6] further claimed the equivalence between GP and deep neural networks when each hidden layer in latter is of infinite width. Consequently, machine learning practitioners can perform Bayesian inference by treating deep and wide neural network as a GP, and exploit the analytic marginal and conditional properties of multivariate Gaussian distribution. Otherwise, one needs to employ gradient-based learning and bootstrap sampling for obtaining predictive distribution [7]. In reality, all neural networks have finite width. Therefore, the deviation from Gaussianity requires further quantitative account as practitioners may wonder the corrections to the predictive mean and variance in, for example, a regression task. Yaida [8] and colleagues [9] proposed a perturbative approach for computing the multivariate cumulants by direct application of Wick's contraction theorem.

Despite the recent advances in open-domain dialogue systems, building a reliable evaluation metric is still a challenging problem. Recent studies proposed learnable metrics based on classification models trained to distinguish the correct response. However, neural classifiers are known to make overly confident predictions for examples from unseen distributions. We propose DEnsity, which evaluates a response by utilizing density estimation on the feature space derived from a neural classifier. Our metric measures how likely a response would appear in the distribution of human conversations. Moreover, to improve the performance of DEnsity, we utilize contrastive learning to further compress the feature space. Experiments on multiple response evaluation datasets show that DEnsity correlates better with human evaluations than the existing metrics. Our code is available at https://github.com/ddehun/DEnsity.