Related papers: Strong identifiability and parameter learning in r…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…
Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…
Reciprocity, or the tendency of individuals to mirror behavior, is a key measure that describes information exchange in a social network. Users in social networks tend to engage in different levels of reciprocal behavior. Differences in…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
Meta-learning has proven to be successful for few-shot learning across the regression, classification, and reinforcement learning paradigms. Recent approaches have adopted Bayesian interpretations to improve gradient-based meta-learners by…
Variational autoencoders and Helmholtz machines use a recognition network (encoder) to approximate the posterior distribution of a generative model (decoder). In this paper we study the necessary and sufficient properties of a recognition…
Survival analysis is a widely-used technique for analyzing time-to-event data in the presence of censoring. In recent years, numerous survival analysis methods have emerged which scale to large datasets and relax traditional assumptions…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in…
Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run…
A mixture of experts models the conditional density of a response variable using a mixture of regression models with covariate-dependent mixture weights. We extend the finite mixture of experts model by allowing the parameters in both the…
As an intrinsic and fundamental property of big data, data heterogeneity exists in a variety of real-world applications, such as precision medicine, autonomous driving, financial applications, etc. For machine learning algorithms, the…
We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes…
This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
This work concerns the development of deep networks that are certifiably robust to adversarial attacks. Joint robust classification-detection was recently introduced as a certified defense mechanism, where adversarial examples are either…
Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider…