Related papers: Enumerating Independent Linear Inferences
We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a…
In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…
Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution.…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a…
An expression is any mathematical formula that contains certain formal variables and operations to be executed in a specified order. In computer science, it is usually convenient to represent each expression in the form of an expression…
The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various…
The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce…
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…
Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition…
We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…
This paper considers an extension of the linear non-Gaussian acyclic model (LiNGAM) that determines the causal order among variables from a dataset when the variables are expressed by a set of linear equations, including noise. In…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine…