The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters $U_1,\dots,U_k$ are mutually independent. Since mutual independence is the target, pairwise similarity measurements are of no use, and thus traditional clustering algorithms are inapplicable. The distribution of the random variables in $S$ is, in general, unknown, but a sample is available. Thus, the problem is cast in terms of time series. Two forms of sampling are considered: i.i.d.\ and stationary time series, with the main emphasis being on the latter, more general, case. A consistent, computationally tractable algorithm for each of the settings is proposed, and a number of open directions for further research are outlined.

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.

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.

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.

In many data exploration tasks it is meaningful to identify groups of attribute interactions that are specific to a variable of interest. For instance, in a dataset where the attributes are medical markers and the variable of interest (class variable) is binary indicating presence/absence of disease, we would like to know which medical markers interact with respect to the binary class label. These interactions are useful in several practical applications, for example, to gain insight into the structure of the data, in feature selection, and in data anonymisation. We present a novel method, based on statistical significance testing, that can be used to verify if the data set has been created by a given factorised class-conditional joint distribution, where the distribution is parametrised by a partition of its attributes. Furthermore, we provide a method, named ASTRID, for automatically finding a partition of attributes describing the distribution that has generated the data. State-of-the-art classifiers are utilised to capture the interactions present in the data by systematically breaking attribute interactions and observing the effect of this breaking on classifier performance. We empirically demonstrate the utility of the proposed method with examples using real and synthetic data.

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.

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.

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.

We propose a probabilistic model to aggregate the answers of respondents answering multiple-choice questions. The model does not assume that everyone has access to the same information, and so does not assume that the consensus answer is correct. Instead, it infers the most probable world state, even if only a minority vote for it. Each respondent is modeled as receiving a signal contingent on the actual world state, and as using this signal to both determine their own answer and predict the answers given by others. By incorporating respondent's predictions of others' answers, the model infers latent parameters corresponding to the prior over world states and the probability of different signals being received in all possible world states, including counterfactual ones. Unlike other probabilistic models for aggregation, our model applies to both single and multiple questions, in which case it estimates each respondent's expertise. The model shows good performance, compared to a number of other probabilistic models, on data from seven studies covering different types of expertise.