Related papers: Function Classes for Identifiable Nonlinear Indepe…
We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in…
Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
This paper deals simultaneously with linear structural and functional error-in-variables models (SEIVM and FEIVM), revisiting in this context generalized and modified least squares estimators of the slope and intercept, and some methods of…
Transformation-based methods have been an attractive approach in non-parametric inference for problems such as unconditional and conditional density estimation due to their unique hierarchical structure that models the data as flexible…
Latent component identification from unknown nonlinear mixtures is a foundational challenge in machine learning, with applications in tasks such as disentangled representation learning and causal inference. Prior work in nonlinear…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…
Adept traffic models are critical to both planning and closed-loop simulation for autonomous vehicles (AV), and key design objectives include accuracy, diverse multimodal behaviors, interpretability, and downstream compatibility. Recently,…
This paper studies the central limit theorems (CLTs) for linear spectral statistics (LSSs) of general sample covariance matrices, when the test functions belong to $C^3$, the class of functions with continuous third order derivatives. We…
Behavioral evaluation is the dominant paradigm for assessing alignment in large language models (LLMs). In current practice, observed compliance under finite evaluation protocols is treated as evidence of latent alignment. However, the…
We show that the mutual information between the representation of a learning machine and the hidden features that it extracts from data is bounded from below by the relevance, which is the entropy of the model's energy distribution. Models…
Object-centric learning (OCL) aims to learn structured scene representations that support compositional generalization and robustness to out-of-distribution (OOD) data. However, OCL models are often not evaluated regarding these goals.…
The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge…
Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential…
Often, when dealing with real-world recognition problems, we do not need, and often cannot have, knowledge of the entire set of possible classes that might appear during operational testing. In such cases, we need to think of robust…
Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…
In-context learning (ICL) has emerged as a powerful paradigm for easily adapting Large Language Models (LLMs) to various tasks. However, our understanding of how ICL works remains limited. We explore a simple model of ICL in a controlled…
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…
Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…