Zobrazeno 1 - 10
of 180
pro vyhledávání: '"Zwiernik P"'
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on its appli
Externí odkaz:
http://arxiv.org/abs/2411.14080
We consider the problem of structure recovery in a graphical model of a tree where some variables are latent. Specifically, we focus on the Gaussian case, which can be reformulated as a well-studied problem: recovering a semi-labeled tree from a dist
Externí odkaz:
http://arxiv.org/abs/2408.15624
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and learning its
Externí odkaz:
http://arxiv.org/abs/2405.10412
Autor:
Zwiernik, Piotr
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance matrix or its
Externí odkaz:
http://arxiv.org/abs/2306.03590
We study a notion of positivity of Gaussian directed acyclic graphical models corresponding to a non-negativity constraint on the coefficients of the associated structural equation model. We prove that this constraint is equivalent to the distributio
Externí odkaz:
http://arxiv.org/abs/2305.19884
We consider two applications where we study how dependence structure between many variables is linked to external network data. We first study the interplay between social media connectedness and the co-evolution of the COVID-19 pandemic across USA c
Externí odkaz:
http://arxiv.org/abs/2210.11107
Autor:
Mesters, Geert, Zwiernik, Piotr
A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this paper we s
Externí odkaz:
http://arxiv.org/abs/2206.13668
Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 ($ \mathrm{MTP}
Externí odkaz:
http://arxiv.org/abs/2112.14727
We study the problem of maximum likelihood estimation given one data sample ($n=1$) over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often used as a null model in phylogenetics, where the one-sample regime is c
Externí odkaz:
http://arxiv.org/abs/2112.00816
Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar et al. showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Their other paper
Externí odkaz:
http://arxiv.org/abs/2102.05472