相关论文: Breaking the curse of dimensionality in structured…
We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and use a new formula for the density of a random variable…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…
In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve…
We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…
The complexity of a graph can be obtained as a derivative of a variation of the zeta function or a partial derivative of its generalized characteristic polynomial evaluated at a point [\textit{J. Combin. Theory Ser. B}, 74 (1998), pp.…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
We propose a new statistical procedure able in some way to overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
Classification models are a key component of structural digital twin technologies used for supporting asset management decision-making. An important consideration when developing classification models is the dimensionality of the input, or…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…
This paper studies a Markov network model for unbalanced data, aiming to solve the problems of classification bias and insufficient minority class recognition ability of traditional machine learning models in environments with uneven class…
We study the difference between the probability density of a random variable $F$ on Markov diffusion chaos and the probability density of a general target distribution $Z$. In the special case where $F$ is a chaotic random variables and $Z$…
Given finite configurations $P_1, \dots, P_n \subset \mathbb{R}^d$, let us denote by $\mathbf{m}_{\mathbb{R}^d}(P_1, \dots, P_n)$ the maximum density a set $A \subseteq \mathbb{R}^d$ can have without containing congruent copies of any…