Related papers: Matrix product representation and synthesis for ra…
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…
Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often…
Evaluating the quality of synthetic data remains a key challenge for ensuring privacy and utility in data-driven research. In this work, we present an evaluation framework that quantifies how well synthetic data replicates original…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
We develop a general framework for incorporating distributional preferences in market design. We identify the structural properties of these preferences that guarantee the path independence of choice rules. In decentralized settings, a…
The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et…
In general, synthesis models provide the mean value of the distribution of possible integrated luminosities, this distribution (and not only its mean value) being the actual description of the integrated luminosity. Therefore, to obtain the…
A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
Time series prediction is a widespread and well studied problem with applications in many domains (medical, geoscience, network analysis, finance, econometry etc.). In the case of multivariate time series, the key to good performances is to…
The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…