Related papers: Three Random Intercepts of a Segment

We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of…

Alignment has quickly become a default ingredient in LLM development, with techniques such as reinforcement learning from human feedback making models act safely, follow instructions, and perform ever-better on complex tasks. While these…

We consider the problem of eliciting expert assessments of an uncertain parameter. The context is risk control, where there are, in fact, three uncertain parameters to be estimates. Two of these are probabilities, requiring the that the…

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

The equality constraint a+b+c=1 for random triangle sides corresponds to breaking a stick in two places. An analog a^2+b^2+c^2=1 has a remarkable feature: the bivariate density for angles coincides with that for 3D Gaussian triangles.…

Machine comprehension, answering a question depending on a given context paragraph is a typical task of Natural Language Understanding. It requires to model complex dependencies existing between the question and the context paragraph. There…

Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…

An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

Ordinal measurements are common outcomes in studies within psychology, as well as in the social and behavioral sciences. Choosing an appropriate regression model for analysing such data poses a difficult task. This paper aims to facilitate…

We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved results, we further improve the limiting distribution of the number of triangles in random regular graphs.

In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on…

Increased adaptability of RNN language models leads to improved predictions that benefit many applications. However, current methods do not take full advantage of the RNN structure. We show that the most widely-used approach to adaptation…

If a line cuts randomly two sides of a triangle, the length of the segment determined by the points of intersection is also random. The object of this study, applied to a particular case, is to calculate the probability that the length of…

Estimating probability distributions which describe where an object is likely to be from camera data is a task with many applications. In this work we describe properties which we argue such methods should conform to. We also design a…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…

A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…

Tree-based ensembles such as the Random Forest are modern classics among statistical learning methods. In particular, they are used for predicting univariate responses. In case of multiple outputs the question arises whether we separately…

We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…