Related papers: On the Upper Limit of Separability
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
Variational mutual information (MI) estimators are widely used in unsupervised representation learning methods such as contrastive predictive coding (CPC). A lower bound on MI can be obtained from a multi-class classification problem, where…
Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Several methods to estimate MI, from samples of two random variables with unknown underlying probability distributions have been…
Mutual Information (MI) is a fundamental measure of statistical dependence widely used in representation learning. While direct optimization of MI via its definition as a Kullback-Leibler divergence (KLD) is often intractable, many recent…
In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…
A first differentiable analysis pipeline is presented for an example high-energy physics (HEP) use case with publicly available collision data from the Compact Muon Solenoid detector at the Large Hadron Collider. The pipeline combines tools…
Computation of Mutual Information (MI) helps understand the amount of information shared between a pair of random variables. Automated feature selection techniques based on MI ranking are regularly used to extract information from sensitive…
Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…
Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given dataset. Privacy restrictions may require the curator of the data or the respondents themselves…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modelling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing…
We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and…