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Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is…
Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…
The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite…
Recently, a plethora of works have proposed inference-time algorithms (e.g. best-of-n), which incorporate verifiers to assist the generation process. Their quality-efficiency trade-offs have been empirically benchmarked on a variety of…
Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary…
We introduce a new family of one factor distributions for high-dimensional binary data. The model provides an explicit probability for each event, thus avoiding the numeric approximations often made by existing methods. Model interpretation…
Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the…
We propose a probabilistic model for interpreting gene expression levels that are observed through single-cell RNA sequencing. In the model, each cell has a low-dimensional latent representation. Additional latent variables account for…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and…
The increasing availability of relational data has contributed to a growing reliance on network-based representations of complex systems. Over time, these models have evolved to capture more nuanced properties, such as the heterogeneity of…
Large-scale natural language generation requires the integration of vast amounts of knowledge: lexical, grammatical, and conceptual. A robust generator must be able to operate well even when pieces of knowledge are missing. It must also be…
In this paper, we present the first structural binarization method for LLM compression to less than 1-bit precision. Although LLMs have achieved remarkable performance, their memory-bound nature during the inference stage hinders the…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
In this paper, we develop a new cellular automata-based linear model for several nonlinear pseudorandom number generators with practical applications in symmetric cryptography. Such a model generates all the solutions of linear binary…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…