Related papers: Optimal structure learning and conditional indepen…
Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…
We consider testing multivariate conditional independence between a response Y and a covariate vector X given additional variables Z. We introduce the Multivariate Sufficient Statistic Conditional Randomization Test (MS-CRT), which…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
Numerous machine learning algorithms contain pairwise statistical problems at their core---that is, tasks that require computations over all pairs of input points if implemented naively. Often, tree structures are used to solve these…
The problem of reinforcement learning is considered where the environment or the model undergoes a change. An algorithm is proposed that an agent can apply in such a problem to achieve the optimal long-time discounted reward. The algorithm…