When recruiting job candidates, employers rarely observe their underlying skill level directly. Instead, they must administer a series of interviews and/or collate other noisy signals in order to estimate the worker's skill. Traditional economics papers address screening models where employers access worker skill via a single noisy signal. In this paper, we extend this theoretical analysis to a multi-test setting, considering both Bernoulli and Gaussian models. We analyze the optimal employer policy both when the employer sets a fixed number of tests per candidate and when the employer can set a dynamic policy, assigning further tests adaptively based on results from the previous tests. To start, we characterize the optimal policy when employees constitute a single group, demonstrating some interesting trade-offs. Subsequently, we address the multi-group setting, demonstrating that when the noise levels vary across groups, a fundamental impossibility emerges whereby we cannot administer the same number of tests, subject candidates to the same decision rule, and yet realize the same outcomes in both groups.

Prevalent theories in cognitive science propose that humans understand and represent the knowledge of the world through causal relationships. In making sense of the world, we build causal models in our mind to encode cause-effect relations of events and use these to explain why new events happen. In this paper, we use causal models to derive causal explanations of behaviour of reinforcement learning agents. We present an approach that learns a structural causal model during reinforcement learning and encodes causal relationships between variables of interest. This model is then used to generate explanations of behaviour based on counterfactual analysis of the causal model. We report on a study with 120 participants who observe agents playing a real-time strategy game (Starcraft II) and then receive explanations of the agents' behaviour. We investigated: 1) participants' understanding gained by explanations through task prediction; 2) explanation satisfaction and 3) trust. Our results show that causal model explanations perform better on these measures compared to two other baseline explanation models.

Infinite-activity completely random measures (CRMs) have become important building blocks of complex Bayesian nonparametric models. They have been successfully used in various applications such as clustering, density estimation, latent feature models, survival analysis or network science. Popular infinite-activity CRMs include the (generalized) gamma process and the (stable) beta process. However, except in some specific cases, exact simulation or scalable inference with these models is challenging and finite-dimensional approximations are often considered. In this work, we propose a general and unified framework to derive both series representations and finite-dimensional approximations of CRMs. Our framework can be seen as an extension of constructions based on size-biased sampling of Poisson point process [Perman1992]. It includes as special cases several known series representations as well as novel ones. In particular, we show that one can get novel series representations for the generalized gamma process and the stable beta process. We also provide some analysis of the truncation error.

Sum-product networks (SPNs) are flexible density estimators and have received significant attention, due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc, and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning. First, we decompose the problem into i) laying out a basic computational graph, and ii) learning the so-called scope function over the graph. The first is rather unproblematic and akin to neural network architecture validation. The second characterises the effective structure of the SPN and needs to respect the usual structural constraints in SPN, i.e. completeness and decomposability. While representing and learning the scope function is rather involved in general, in this paper, we propose a natural parametrisation for an important and widely used special case of SPNs. These structural parameters are incorporated into a Bayesian model, such that simultaneous structure and parameter learning is cast into monolithic Bayesian posterior inference. In various experiments, our Bayesian SPNs often improve test likelihoods over greedy SPN learners. Further, since the Bayesian framework protects against overfitting, we are able to evaluate hyper-parameters directly on the Bayesian model score, waiving the need for a separate validation set, which is especially beneficial in low data regimes. Bayesian SPNs can be applied to heterogeneous domains and can easily be extended to nonparametric formulations. Moreover, our Bayesian approach is the first which consistently and robustly learns SPN structures under missing data.

Differential privacy is a mathematical framework for privacy-preserving data analysis. Changing the hyperparameters of a differentially private algorithm allows one to trade off privacy and utility in a principled way. Quantifying this trade-off in advance is essential to decision-makers tasked with deciding how much privacy can be provided in a particular application while keeping acceptable utility. For more complex tasks, such as training neural networks under differential privacy, the utility achieved by a given algorithm can only be measured empirically. This paper presents a Bayesian optimization methodology for efficiently characterizing the privacy-utility trade-off of any differentially private algorithm using only empirical measurements of its utility. The versatility of our method is illustrated on a number of machine learning tasks involving multiple models, optimizers, and datasets.

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models are rarely well-specified in practice. In this work, we study VB under model misspecification. We prove the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution. Moreover, the VB posterior mean centers at the same value and is also asymptotically normal. These results generalize the variational Bernstein--von Mises theorem [29] to misspecified models. As a consequence of these results, we find that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family. As illustrations, we study VB under three forms of model misspecification, ranging from model over-/under-dispersion to latent dimensionality misspecification. We conduct two simulation studies that demonstrate the theoretical results.

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify causal structure and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods.

The traditional directed acyclic graph (DAG) model assumes data are generated independently from the underlying joint distribution defined by the DAG. In many applications, however, individuals are linked via a network and thus the independence assumption does not hold. We propose a novel Gaussian DAG model for network data, where the dependence among individual data points (row covariance) is modeled by an undirected graph. Under this model, we develop a maximum penalized likelihood method to estimate the DAG structure and the row correlation matrix. The algorithm iterates between a decoupled lasso regression step and a graphical lasso step. We show with extensive simulated and real network data, that our algorithm improves the accuracy of DAG structure learning by leveraging the information from the estimated row correlations. Moreover, we demonstrate that the performance of existing DAG learning methods can be substantially improved via de-correlation of network data with the estimated row correlation matrix from our algorithm.

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model uncertainty. Variational methods have been used for approximating intractable integrals that arise in Bayesian inference for neural networks. In this report, we review the major variational inference concepts pertinent to Bayesian neural networks and compare various approximation methods used in literature. We also talk about the applications of variational bayes in Reinforcement learning and continual learning.

The exposure bias problem refers to the training-inference discrepancy caused by teacher forcing in maximum likelihood estimation (MLE) training for recurrent neural network language models (RNNLM). It has been regarded as a central problem for natural language generation (NLG) model training. Although a lot of algorithms have been proposed to avoid teacher forcing and therefore to remove exposure bias, there is little work showing how serious the exposure bias problem is. In this work, starting from the definition of exposure bias, we propose two simple and intuitive approaches to quantify exposure bias for MLE-trained language models. Experiments are conducted on both synthetic and real data-sets. Surprisingly, our results indicate that either exposure bias is trivial (i.e. indistinguishable from the mismatch between model and data distribution), or is not as significant as it is presumed to be (with a measured performance gap of 3%). With this work, we suggest re-evaluating the viewpoint that teacher forcing or exposure bias is a major drawback of MLE training.