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We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise…
The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I…
We analyse the metastable behaviour of the dilute Curie-Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are Bernoulli random variables with mean $p\in…
We show that phase transitions in Ising systems with planar defects, i.e., disorder perfectly correlated in two dimensions are destroyed by smearing. This is caused by effects similar to but stronger than the Griffiths phenomena:…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…
We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…
The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
Knowledge about existence, strength, and dominant direction of causal influences is of paramount importance for understanding complex systems. With limited amounts of realistic data, however, current methods for investigating causal links…
In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose…
Weak measurements have been predicted to dramatically alter universal properties of quantum critical wavefunctions, though experimental validation remains an open problem. Here we devise a practical scheme for realizing measurement-altered…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…