Related papers: Sequential Kernelized Independence Testing
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…
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…
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…
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…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
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…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…
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…
The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…
The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an…
We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…
Recently, the importance of analysing data and collecting valuable insight efficiently has been increasing in various fields. Estimating mutual information (MI) plays a critical role to investigate the relationship among multiple random…
In online multiple testing, an a priori unknown number of hypotheses are tested sequentially, i.e. at each time point a test decision for the current hypothesis has to be made using only the data available so far. Although many powerful…
We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…