相关论文: Conditional independence relations and log-linear …
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional…
Probabilistic modeling is one of the foundations of modern machine learning and artificial intelligence. In this paper, we propose a novel type of probabilistic models named latent dependency forest models (LDFMs). A LDFM models the…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…
Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model…
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy called cyclic-Boolean independence. We investigate formulas…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…
Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given…
Starting from elementary considerations about independence and Markov processes in classical probability we arrive at the new concept of conditional monotone independence (or operator-valued monotone independence). With the help of product…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact…
We propose a method that represents language models by log-likelihood vectors over prompt-response pairs and constructs model maps for comparing their conditional distributions. In this space, distances between models approximate the KL…