Related papers: Likelihood-Preserving Embeddings for Statistical I…

In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…

We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…

Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…

Manifold learning techniques, such as Locally linear embedding (LLE), are designed to preserve the local neighborhood structures of high-dimensional data during dimensionality reduction. Traditional LLE employs Euclidean distance to define…

This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…

Let $n$ be a positive integer. We provide an explicit geometrically motivated $1$-Lipschitz map from the space of persistence diagrams on $n$ points (equipped with the Bottleneck distance) into the Hilbert space $\ell^2$. Such maps are a…

This paper introduces a first implementation of a novel likelihood-ratio-based approach for constructing confidence intervals for neural networks. Our method, called DeepLR, offers several qualitative advantages: most notably, the ability…

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…

Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…

A major challenge in designing efficient statistical supervised learning algorithms is finding representations that perform well not only on available training samples but also on unseen data. While the study of representation learning has…

The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…

Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream…

Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures…

Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their…

In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, almost surely, (1) the likelihood function is bounded…

Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the…

Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the…