Related papers: Symbolic Density Estimation for Discrete Distribut…
In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…
Growing interest in modelling complex systems from brains to societies to cities using networks has led to increased efforts to describe generative processes that explain those networks. Recent successes in machine learning have prompted…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
Combining discrete probability distributions and combinatorial optimization problems with neural network components has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
Conditional density estimation is a fundamental problem in statistics, with scientific and practical applications in biology, economics, finance and environmental studies, to name a few. In this paper, we propose a conditional density…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…
Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…
Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of…
This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…
In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE)…