Related papers: Identifiability-Guaranteed Simplex-Structured Post…
Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in…
Since its introduction, unsupervised representation learning has attracted a lot of attention from the research community, as it is demonstrated to be highly effective and easy-to-apply in tasks such as dimension reduction, clustering,…
Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…
This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian…
In spatial blind source separation the observed multivariate random fields are assumed to be mixtures of latent spatially dependent random fields. The objective is to recover latent random fields by estimating the unmixing transformation.…
We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to…
The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and…
In many machine learning tasks, learning a good representation of the data can be the key to building a well-performant solution. This is because most learning algorithms operate with the features in order to find models for the data. For…
Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or…
The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been…
Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we…
Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they…
A key goal of unsupervised representation learning is "inverting" a data generating process to recover its latent properties. Existing work that provably achieves this goal relies on strong assumptions on relationships between the latent…
Recent advances in nonlinear Independent Component Analysis (ICA) provide a principled framework for unsupervised feature learning and disentanglement. The central idea in such works is that the latent components are assumed to be…
Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…