Related papers: Parameter Estimation in DAGs from Incomplete Data …
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG…
Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…
Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…
Recent work in graph models has found that probabilistic hyperedge replacement grammars (HRGs) can be extracted from graphs and used to generate new random graphs with graph properties and substructures close to the original. In this paper,…
This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We…
Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account…
A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of…
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…
Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to…
This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function $f$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…