Meta-learning can successfully acquire useful inductive biases from data, especially when a large number of meta-tasks are available. Yet, its generalization properties to unseen tasks are poorly understood. Particularly if the number of meta-tasks is small, this raises concerns for potential overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning with unbounded loss functions and Bayesian base learners. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-regularization. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes as base learners, the resulting approach consistently outperforms several popular meta-learning methods, both in terms of predictive accuracy and the quality of its uncertainty estimates.

This problem arises in many cases in machine learning, most notably in large-scale (mini-batch) Bayesian inference (Welling and Teh, 2011, Ahn et al., 2012) and nonconvex stochastic optimization (Raginsky et al., 2017). For the setting of Bayesian inference, one is interested in sampling from a posterior probability measure where U corresponds to the sum of the log-likelihood and the log-prior. For the nonconvex optimization, U(·) is the nonconvex cost function to be minimized. For large values ofβ, a sample from the target measure (1) is an approximate minimizer of the potential U (Raginsky et al., 2017). Consequently, nonasymptotic error bounds for the schemes, which are designed to sample from (1), can be used to obtain guarantees for Bayesian inference or nonconvex optimization. Sampling from a measure of the form (1) is also central in statistical physics (Binder et al., 1993), most notably in molecular dynamics Haile (1992).

Companies may be achieving only a third of the value they could be getting from data science in industry applications. In this paper, we propose a methodology for categorizing and answering 'The Big Three' questions (what is going on, what is causing it, and what actions can I take that will optimize what I care about) using data science. The applications of data science seem to be nearly endless in today's modern landscape, with each company jockeying for position in the new data and insights economy. Yet, data scientists seem to be solely focused on using classification, regression, and clustering methods to answer the question 'what is going on'. Answering questions about why things are happening or how to take optimal actions to improve metrics are relegated to niche fields of research and generally neglected in industry data science analysis. We survey technical methods to answer these other important questions, describe areas in which some of these methods are being applied, and provide a practical example of how to apply our methodology and selected methods to a real business use case.

In this work, we propose learnable Bernoulli dropout (LBD), a new model-agnostic dropout scheme that considers the dropout rates as parameters jointly optimized with other model parameters. By probabilistic modeling of Bernoulli dropout, our method enables more robust prediction and uncertainty quantification in deep models. Especially, when combined with variational auto-encoders (VAEs), LBD enables flexible semi-implicit posterior representations, leading to new semi-implicit VAE~(SIVAE) models. We solve the optimization for training with respect to the dropout parameters using Augment-REINFORCE-Merge (ARM), an unbiased and low-variance gradient estimator. Our experiments on a range of tasks show the superior performance of our approach compared with other commonly used dropout schemes. Overall, LBD leads to improved accuracy and uncertainty estimates in image classification and semantic segmentation. Moreover, using SIVAE, we can achieve state-of-the-art performance on collaborative filtering for implicit feedback on several public datasets.

Bayesian optimisation is a powerful method for non-convex black-box optimization in low data regimes. However, the question of establishing tight upper bounds for common algorithms in the noiseless setting remains a largely open question. In this paper, we establish new and tightest bounds for two algorithms, namely GP-UCB and Thompson sampling, under the assumption that the objective function is smooth in terms of having a bounded norm in a Mat\'ern RKHS. Importantly, unlike several related works, we do not consider perfect knowledge of the kernel of the Gaussian process emulator used within the Bayesian optimization loop. This allows us to provide results for practical algorithms that sequentially estimate the Gaussian process kernel parameters from the available data.

Smarter applications are making better use of the insights gleaned from data, having an impact on every industry and research discipline. At the core of this revolution lies the tools and the methods that are driving it, from processing the massive piles of data generated each day to learning from and taking useful action. Deep neural networks, along with advancements in classical ML and scalable general-purpose GPU computing, have become critical components of artificial intelligence, enabling many of these astounding breakthroughs and lowering the barrier to adoption. Python continues to be the most preferred language for scientific computing, data science, and machine learning, boosting both performance and productivity by enabling the use of low-level libraries and clean high-level APIs. This survey offers insight into the field of machine learning with Python, taking a tour through important topics to identify some of the core hardware and software paradigms that have enabled it. We cover widely-used libraries and concepts, collected together for holistic comparison, with the goal of educating the reader and driving the field of Python machine learning forward.

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.

Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience of the network users. We focus on Bayesian games with atomic players, where network vagaries are modeled via a (random) state of nature which determines the costs incurred by the players. A third-party entity---the sender---can observe the realized state of the network and exploit this additional information to send a signal to each player. A natural question is the following: is it possible for an informed sender to reduce the overall social cost via the strategic provision of information to players who update their beliefs rationally? The paper focuses on the problem of computing optimal ex ante persuasive signaling schemes, showing that symmetry is a crucial property for its solution. Indeed, we show that an optimal ex ante persuasive signaling scheme can be computed in polynomial time when players are symmetric and have affine cost functions. Moreover, the problem becomes NP-hard when players are asymmetric, even in non-Bayesian settings.

We present a conversational recommendation system based on a Bayesian approach. A probability mass function over the items is updated after any interaction with the user, with information-theoretic criteria optimally shaping the interaction and deciding when the conversation should be terminated and the most probable item consequently recommended. Dedicated elicitation techniques for the prior probabilities of the parameters modeling the interactions are derived from basic structural judgements. Such prior information can be combined with historical data to discriminate items with different recommendation histories. A case study based on the application of this approach to \emph{stagend.com}, an online platform for booking entertainers, is finally discussed together with an empirical analysis showing the advantages in terms of recommendation quality and efficiency.

Cost-effectiveness analyses (CEAs) are at the center of health economic decision making. While these analyses help policy analysts and economists determine coverage, inform policy, and guide resource allocation, they are statistically challenging for several reasons. Cost and effectiveness are correlated and follow complex joint distributions which cannot be captured parametrically. Effectiveness (often measured as increased survival time) and cost both tend to be right-censored. Moreover, CEAs are often conducted using observational data with non-random treatment assignment. Policy-relevant causal estimation therefore requires robust confounding control. Finally, current CEA methods do not address cost-effectiveness heterogeneity in a principled way - opting to either present marginal results or cost-effectiveness results for pre-specified subgroups. Motivated by these challenges, we develop a nonparametric Bayesian model for joint cost-survival distributions in the presence of censoring. Our approach utilizes an Enriched Dirichlet Process prior on the covariate effects of cost and survival time, while using a separate Gamma Process prior on the baseline survival time hazard. Causal CEA estimands are identified and estimated via a Bayesian nonparametric g-computation procedure. Finally, we propose leveraging the induced clustering of the Enriched Dirichlet Process to adaptively discover subgroups of patients with different cost-effectiveness profiles. We outline an MCMC procedure for full posterior inference, evaluate frequentist properties via simulations, and apply our model to an observational study of endometrial cancer therapies using medical insurance claims data.