Model misspecification is a major consideration in applications of statistical methods and machine learning. However, it is often neglected in contextual bandits. This paper studies a common form of misspecification, an inter-arm heterogeneity that is not captured by context. To address this issue, we assume that the heterogeneity arises due to arm-specific random variables, which can be learned. We call this setting a robust contextual bandit. The arm-specific variables explain the unknown inter-arm heterogeneity, and we incorporate them in the robust contextual estimator of the mean reward and its uncertainty. We develop two efficient bandit algorithms for our setting: a UCB algorithm called RoLinUCB and a posterior-sampling algorithm called RoLinTS. We analyze both algorithms and bound their $n$-round Bayes regret. Our experiments show that RoLinTS is comparably statistically efficient to the classic methods when the misspecification is low, more robust when the misspecification is high, and significantly more computationally efficient than its naive implementation.

Distributed fuzzy neural networks (DFNNs) have attracted increasing attention recently due to their learning abilities in handling data uncertainties in distributed scenarios. However, it is challenging for DFNNs to handle cases in which the local data are non-independent and identically distributed (non-IID). In this paper, we propose a federated fuzzy neural network (FedFNN) with evolutionary rule learning (ERL) to cope with non-IID issues as well as data uncertainties. The FedFNN maintains a global set of rules in a server and a personalized subset of these rules for each local client. ERL is inspired by the theory of biological evolution; it encourages rule variations while activating superior rules and deactivating inferior rules for local clients with non-IID data. Specifically, ERL consists of two stages in an iterative procedure: a rule cooperation stage that updates global rules by aggregating local rules based on their activation statuses and a rule evolution stage that evolves the global rules and updates the activation statuses of the local rules. This procedure improves both the generalization and personalization of the FedFNN for dealing with non-IID issues and data uncertainties. Extensive experiments conducted on a range of datasets demonstrate the superiority of the FedFNN over state-of-the-art methods.

We propose a method for maximum likelihood estimation of path choice model parameters and arc travel time using data of different levels of granularity. Hitherto these two tasks have been tackled separately under strong assumptions. Using a small example, we illustrate that this can lead to biased results. Results on both real (New York yellow cab) and simulated data show strong performance of our method compared to existing baselines.

Imputation allows datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost through imputation. The missing-indicator approach can be used to preserve this information. There are several theoretical considerations why missing-indicators may or may not be beneficial, but there has not been any large-scale practical experiment on real-life datasets to test this question for machine learning predictions. We perform this experiment for three imputation strategies and a range of different classification algorithms, on the basis of twenty real-life datasets. We find that missing-indicators generally increase classification performance, and that nearest neighbour and iterative imputation do not lead to better performance than simple mean/mode imputation. Therefore, we recommend the use of missing-indicators with mean/mode imputation as a safe default, with the caveat that for decision trees, pruning is necessary to prevent overfitting.

In NMT we search for the mode of the model distribution to form predictions. The mode and other high-probability translations found by beam search have been shown to often be inadequate in a number of ways. This prevents improving translation quality through better search, as these idiosyncratic translations end up selected by the decoding algorithm, a problem known as the beam search curse. Recently, an approximation to minimum Bayes risk (MBR) decoding has been proposed as an alternative decision rule that would likely not suffer from the same problems. We analyse this approximation and establish that it has no equivalent to the beam search curse. We then design approximations that decouple the cost of exploration from the cost of robust estimation of expected utility. This allows for much larger hypothesis spaces, which we show to be beneficial. We also show that mode-seeking strategies can aid in constructing compact sets of promising hypotheses and that MBR is effective in identifying good translations in them. We conduct experiments on three language pairs varying in amounts of resources available: English into and from German, Romanian, and Nepali.

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic partial differential equations, such as the pressure Poisson equation (PPE) in incompressible fluid flows, distance localization cannot be applied, as we cannot disentangle slowly decaying physical interactions from spurious long-range correlations. This is particularly true for the PPE, in which distant vortex elements couple nonlinearly to induce pressure. Instead, these inverse problems have a low effective dimension: low-dimensional projections of the observations strongly inform a low-dimensional subspace of the state space. We derive a low-rank factorization of the Kalman gain based on the spectrum of the Jacobian of the observation operator. The identified eigenvectors generalize the source and target modes of the multipole expansion, independently of the underlying spatial distribution of the problem. Given rapid spectral decay, inference can be performed in the low-dimensional subspace spanned by the dominant eigenvectors. This low-rank EnKF is assessed on dynamical systems with Poisson observation operators, where we seek to estimate the positions and strengths of point singularities over time from potential or pressure observations. We also comment on the broader applicability of this approach to elliptic inverse problems outside the context of filtering.

There has been an increasing interest in utilizing machine learning methods in inverse problems and imaging. Most of the work has, however, concentrated on image reconstruction problems, and the number of studies regarding the full solution of the inverse problem is limited. In this work, we study a machine learning based approach for the Bayesian inverse problem of photoacoustic tomography. We develop an approach for estimating the posterior distribution in photoacoustic tomography using an approach based on the variational autoencoder. The approach is evaluated with numerical simulations and compared to the solution of the inverse problem using a Bayesian approach.

Score matching (SM) is a convenient method for training flexible probabilistic models, which is often preferred over the traditional maximum-likelihood (ML) approach. However, these models are less interpretable than normalized models; as such, training robustness is in general difficult to assess. We present a critical study of existing variational SM objectives, showing catastrophic failure on a wide range of datasets and network architectures. Our theoretical insights on the objectives emerge directly from their equivalent autoencoding losses when optimizing variational autoencoder (VAE) models. First, we show that in the Fisher autoencoder, SM produces far worse models than maximum-likelihood, and approximate inference by Fisher divergence can lead to low-density local optima. However, with important modifications, this objective reduces to a regularized autoencoding loss that resembles the evidence lower bound (ELBO). This analysis predicts that the modified SM algorithm should behave very similarly to ELBO on Gaussian VAEs. We then review two other FD-based objectives from the literature and show that they reduce to uninterpretable autoencoding losses, likely leading to poor performance. The experiments verify our theoretical predictions and suggest that only ELBO and the baseline objective robustly produce expected results, while previously proposed SM methods do not.

Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive Models (AO-ARMs) -- closely related to popular models such as BERT and XLNet -- has shown breakthrough performance in arbitrary conditional tasks across a sweeping range of domains. But, in spite of their success, in this paper we identify significant improvements to be made to previous formulations of AO-ARMs. First, we show that AO-ARMs suffer from redundancy in their probabilistic model, i.e., they define the same distribution in multiple different ways. We alleviate this redundancy by training on a smaller set of univariate conditionals that still maintains support for efficient arbitrary conditional inference. Second, we upweight the training loss for univariate conditionals that are evaluated more frequently during inference. Our method leads to improved performance with no compromises on tractability, giving state-of-the-art likelihoods in arbitrary conditional modeling on text (Text8), image (CIFAR10, ImageNet32), and continuous tabular data domains.

Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level causal variables are given. However, in machine learning tasks, one often operates on low-level data like image pixels or high-dimensional vectors. In such settings, the entire Structural Causal Model (SCM) -- structure, parameters, \textit{and} high-level causal variables -- is unobserved and needs to be learnt from low-level data. We treat this problem as Bayesian inference of the latent SCM, given low-level data. For linear Gaussian additive noise SCMs, we present a tractable approximate inference method which performs joint inference over the causal variables, structure and parameters of the latent SCM from random, known interventions. Experiments are performed on synthetic datasets and a causally generated image dataset to demonstrate the efficacy of our approach. We also perform image generation from unseen interventions, thereby verifying out of distribution generalization for the proposed causal model.