相关论文: On discrimination between classes of distribution …
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences…
We ask: Can focusing on likely classes of a single, in-domain sample improve model predictions? Prior work argued ``no''. We put forward a novel rationale in favor of ``yes'': Sharedness of features among classes indicates their reliability…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
Distributions of the same type can be discussed in terms of distribution functions as well as their integral transforms. For continuous distributions they are equivalent. In this note it is shown that it is not so in the discrete case.
The problem of estimating a proportion of objects with particular attribute in a finite population is considered. This paper shows an example of the application of estimation fraction using new proposed sample allocation in a population…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Suppose $F$ is a distribution on the half-line $[0,\infty)$. We study the limits of the ratios of tails $\bar{F*F}(x)/\bar{F}(x)$ as $x\to\infty$. We also discuss the classes of distributions ${\mathcal{S}}$, ${\mathcal{S}}(\gamma)$ and…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In the typical setting investigated till now, each classifier is trained…
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…
In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…
A basic question in learning theory is to identify if two distributions are identical when we have access only to examples sampled from the distributions. This basic task is considered, for example, in the context of Generative Adversarial…