We study the use of randomized value functions to guide deep exploration in reinforcement learning. This offers an elegant means for synthesizing statistically and computationally efficient exploration with common practical approaches to value function learning. We present several reinforcement learning algorithms that leverage randomized value functions and demonstrate their efficacy through computational studies. We also prove a regret bound that establishes statistical efficiency with a tabular representation.

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.

It is generally accepted that all models are wrong -- the difficulty is determining which are useful. Here, a useful model is considered as one that is capable of combining data and expert knowledge, through an inversion or calibration process, to adequately characterize the uncertainty in predictions of interest. This paper derives conditions that specify which simplified models are useful and how they should be calibrated. To start, the notion of an optimal simplification is defined. This relates the model simplifications to the nature of the data and predictions, and determines when a standard probabilistic calibration scheme is capable of accurately characterizing uncertainty. Furthermore, two additional conditions are defined for suboptimal models that determine when the simplifications can be safely ignored. The first allows a suboptimally simplified model to be used in a way that replicates the performance of an optimal model. This is achieved through the judicial selection of a prior term for the calibration process that explicitly includes the nature of the data, predictions and modelling simplifications. The second considers the dependency structure between the predictions and the available data to gain insights into when the simplifications can be overcome by using the right calibration data. Furthermore, the derived conditions are related to the commonly used calibration schemes based on Tikhonov and subspace regularization. To allow concrete insights to be obtained, the analysis is performed under a linear expansion of the model equations and where the predictive uncertainty is characterized via second order moments only.

During the past decade, several areas of speech and language understanding have witnessed substantial breakthroughs from the use of data-driven models. In the area of dialogue systems, the trend is less obvious, and most practical systems are still built through significant engineering and expert knowledge. Nevertheless, several recent results suggest that data-driven approaches are feasible and quite promising. To facilitate research in this area, we have carried out a wide survey of publicly available datasets suitable for data-driven learning of dialogue systems. We discuss important characteristics of these datasets, how they can be used to learn diverse dialogue strategies, and their other potential uses. We also examine methods for transfer learning between datasets and the use of external knowledge. Finally, we discuss appropriate choice of evaluation metrics for the learning objective.

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi, Reingold and Roth introduced one potential model and proposed several solutions based on differential privacy. In previous work in 2016, we described a problem with this model and instead proposed a Bayesian variant, but also found that the analogous Bayesian methods cannot achieve the same statistical guarantees as in the static case. In this paper, we prove the first positive results for the Bayesian model, showing that with a Dirichlet prior, the posterior mean algorithm indeed matches the statistical guarantees of the static case. The main ingredient is a new theorem showing that the $\mathrm{Beta}(\alpha,\beta)$ distribution is subgaussian with variance proxy $O(1/(\alpha+\beta+1))$, a concentration result also of independent interest. We provide two proofs of this result: a probabilistic proof utilizing a simple condition for the raw moments of a positive random variable and a learning-theoretic proof based on considering the beta distribution as a posterior, both of which have implications to other related problems.

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is commonly performed in practice, as an iterative process of interacting repeatedly with the same data set, such as repeated tests against a holdout set. Previous work has defined a model with a rather strong lower bound on sample complexity in terms of the number of queries, $n\sim\sqrt q$, arguing that adaptive data analysis is much harder than static data analysis, where $n\sim\log q$ is possible. Instead, we argue that those strong lower bounds point to a limitation of the previous model in that it must consider wildly asymmetric scenarios which do not hold in typical applications. To better understand other difficulties of adaptivity, we propose a new Bayesian version of the problem that mandates symmetry. Since the other lower bound techniques are ruled out, we can more effectively see difficulties that might otherwise be overshadowed. As a first contribution to this model, we produce a new problem using error-correcting codes on which a large family of methods, including all previously proposed algorithms, require roughly $n\sim\sqrt[4]q$. These early results illustrate new difficulties in adaptive data analysis regarding slightly correlated queries on problems with concentrated uncertainty.

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statistics are known, it is unclear which guiding principles can be used to construct effective summary statistics. In this paper we explore the possibility of automating the process of constructing summary statistics by training deep neural networks to predict the parameters from artificially generated data: the resulting summary statistics are approximately posterior means of the parameters. With minimal model-specific tuning, our method constructs summary statistics for the Ising model and the moving-average model, which match or exceed theoretically-motivated summary statistics in terms of the accuracies of the resulting posteriors.

A common applied statistics task involves building regression models to characterize non-linear relationships between variables. It is possible to fit such models by assuming a particular non-linear functional form, such as a sinusoidal, exponential, or polynomial function, to describe one variable's response to the variation in another. Unless this relationship is obvious from the outset, however, it involves possibly extensive model selection procedures to ensure the most appropriate model is retained. Alternatively, a non-parametric approach can be adopted by defining a set of knots across the variable space and use a spline or kernel regression to describe arbitrary non-linear relationships. However, knot layout procedures are somewhat ad hoc and can also involve variable selection. A third alternative is to adopt a Bayesian non-parametric strategy, and directly model the unknown underlying function.

Active search (AS) on graphs focuses on collecting certain labeled nodes (targets) given global knowledge of the network topology and its edge weights under a query budget. However, in most networks, nodes, topology and edge weights are all initially unknown. We introduce selective harvesting, a variant of AS where the next node to be queried must be chosen among the neighbors of the current queried node set; the available training data for deciding which node to query is restricted to the subgraph induced by the queried set (and their node attributes) and their neighbors (without any node or edge attributes). Therefore, selective harvesting is a sequential decision problem, where we must decide which node to query at each step. A classifier trained in this scenario suffers from a tunnel vision effect: without recourse to independent sampling, the urge to query promising nodes forces classifiers to gather increasingly biased training data, which we show significantly hurts the performance of AS methods and standard classifiers. We find that it is possible to collect a much larger set of targets by using multiple classifiers, not by combining their predictions as an ensemble, but switching between classifiers used at each step, as a way to ease the tunnel vision effect. We discover that switching classifiers collects more targets by (a) diversifying the training data and (b) broadening the choices of nodes that can be queried next. This highlights an exploration, exploitation, and diversification trade-off in our problem that goes beyond the exploration and exploitation duality found in classic sequential decision problems. From these observations we propose D3TS, a method based on multi-armed bandits for non-stationary stochastic processes that enforces classifier diversity, matching or exceeding the performance of competing methods on seven real network datasets in our evaluation.

Sejun Park Eunho Y ang † Jinwoo Shin November 4, 2017 Abstract Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are popularly used in practice, but they are typically stuck in local optima. In the recent years, the method of moments have provided a refreshing angle for resolving the non-convex issue, but it is applicable to a quite limited class of latent GMs. In this paper, we aim for enhancing its power via enlarging such a class of latent GMs. To this end, we introduce two novel concepts, coined marginalization and conditioning, which can reduce the problem of learning a larger GM to that of a smaller one. More importantly, they lead to a sequential learning framework that repeatedly increases the learning portion of given latent GM, and thus covers a significantly broader and more complicated class of loopy latent GMs which include convolutional and random regular models. 1 Introduction Graphical models (GM) are succinct representation of a joint distribution on a graph where each node corresponds to a random variable and each edge represents the conditional independence between random variables. GM have been successfully applied for various fields including information theory [12, 19], physics [24] and machine learning [18, 11]. Introducing latent variables to GM has been popular approaches for enhancing their representation powers in recent deep models, e.g., convolutional/restricted/deep Boltzmann machines [20, 27]. Furthermore, they are inevitable in certain scenarios when a part of samples is missing, e.g., see [10]. However, learning parameters of latent GMs is significantly harder than that of no-latent ones since the latent variables make the corresponding negative log-likelihood non-convex.