Related papers: On Identifying a Massive Number of Distributions

Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models…

I tackle the problem of partitioning a sequence into homogeneous segments, where homogeneity is defined by a set of Markov models. The problem is to study the likelihood that a sequence is divided into a given number of segments. Here, the…

By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…

In this paper we consider the problem of segmenting $n$ aligned random sequences of equal length $m$, into a finite number of independent blocks. We propose to use a penalized maximum likelihood criterion to infer simultaneously the number…

Continuous-time event sequences represent discrete events occurring in continuous time. Such sequences arise frequently in real-life. Usually we expect the sequences to follow some regular pattern over time. However, sometimes these…

We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…

Multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We discuss the possible sources of these oscillations and their impact on our…

In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…

In using observed data to make inferences about a population quantity, it is commonly assumed that the sampling distribution from which the data were drawn belongs to a given parametric family of distributions, or at least, a given finite…

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

Let $X$ be a random variable with distribution function $F,$ and $X_{1},X_{2},...,X_{n}$ are independent copies of $X.$ Consider the order statistics $X_{i:n},$ $i=1,2,...,n$ and denote $F_{i:n}(x)=P\{X_{i:n}\leq x\}.$ Using majorization…

A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…

A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

We consider the two related problems of detecting if an example is misclassified or out-of-distribution. We present a simple baseline that utilizes probabilities from softmax distributions. Correctly classified examples tend to have greater…

Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on…

Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random…

For $n \in \mathbb{N}$ and $\varepsilon > 0$, given a sufficiently long sequence of events in a probability space all of measure at least $\varepsilon$, some $n$ of them will have a common intersection. A more subtle pattern: for any $0 < p…

We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…