相关论文: Input-output equivalence and identifiability: some…

Providing explanations for deep neural networks (DNNs) is essential for their use in domains wherein the interpretability of decisions is a critical prerequisite. Despite the plethora of work on interpreting DNNs, most existing solutions…

We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…

The identifiability problem for interventions aims at assessing whether the total effect of some given interventions can be written with a do-free formula, and thus be computed from observational data only. We study this problem,…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases,…

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…

Deep Generative Models (DGMs) are versatile tools for learning data representations while adequately incorporating domain knowledge such as the specification of conditional probability distributions. Recently proposed DGMs tackle the…

We consider an index model of dyadic link formation with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results in a single large network setting for the potentially nonparametric…

Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…

This paper introduces a multiple-input discrete Urysohn operator for modelling non-linear control systems and a technique of its identification by processing the observed input and output signals. It is shown that, due to the nature of the…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

Parameter identifiability refers to the capability of accurately inferring the parameter values of a model from its observations (data). Traditional analysis methods exploit analytical properties of the closed form model, in particular…

Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…

This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…

In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system…

We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…

Similarity-based method gives rise to a new class of methods for multi-label learning and also achieves promising performance. In this paper, we generalize this method, resulting in a new framework for classification task. Specifically, we…

Computational models of complex systems are usually elaborate and sensitive to implementation details, characteristics which often affect their verification and validation. Model replication is a possible solution to this issue. It avoids…

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every…

We consider a model identification problem in which an outcome variable contains nonignorable missing values. Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable…