Related papers: Symbolic Density Estimation for Discrete Distribut…
Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…
This work advances distribution recovery from sparse data and ensemble classification through three main contributions. First, we introduce a closed-form estimator that reconstructs scaled beta distributions from limited statistics…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
Perhaps surprisingly, recent studies have shown probabilistic model likelihoods have poor specificity for out-of-distribution (OOD) detection and often assign higher likelihoods to OOD data than in-distribution data. To ameliorate this…
This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach…
We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying…
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…
Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…
In this paper, we use a stochastic partial differential equation (SPDE) as a model for the density of a population under the influence of random external forces/stimuli given by the environment. We study statistical properties for two…
A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number…
We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
We consider the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in a wireless sensor network (WSN), where each sensor receives a single snapshot of the field. We assume that the observation…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…
A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is…
Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the…
In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…