Related papers: Group-Theoretic Structure Governing Identifiabilit…
In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
We consider recovering causal structure from multivariate observational data. We assume the data arise from a linear structural equation model (SEM) in which the idiosyncratic errors are allowed to be dependent in order to capture possible…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be…
In this paper we prove theorems characterizing the decomposition of equivariant feature spaces, filters and a structural preservation theorem for invariant subspace chains in group equivariant convolutional neural networks(G-CNN).…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…
The tensor square conjecture states that for $n \geq 10$, there is an irreducible representation $V$ of the symmetric group $S_n$ such that $V \otimes V$ contains every irreducible representation of $S_n$. Our main result is that for large…
This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…
Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…
Learning causal effects from data is a fundamental and well-studied problem across science, especially when the cause-effect relationship is static in nature. However, causal effect is less explored when there are dynamical dependencies,…
We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…
In this paper, we investigate a new framework for image classification that adaptively generates spatial representations. Our strategy is based on a sequential process that learns to explore the different regions of any image in order to…
Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
Causal representation learning (CRL) seeks to uncover meaningful latent variables and their corresponding causal structure from high-dimensional observational data. Although its significance, CRL identifiability remains a crucial property,…
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…
This paper proves a representation theorem regarding sequences of random elements that take values in a Borel space and are measurable with respect to the sigma algebra generated by an arbitrary union of sigma algebras. This, together with…