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Large Language Models (LLMs) have reshaped our world with significant advancements in science, engineering, and society through applications ranging from scientific discoveries and medical diagnostics to Chatbots. Despite their ubiquity and…
The distribution of subpopulations is an important property hidden within a dataset. Uncovering and analyzing the subpopulation distribution within datasets provides a comprehensive understanding of the datasets, standing as a powerful tool…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
Latent class analysis, a fundamental problem in categorical data analysis, often encounters overlapping latent classes that introduce further challenges. This paper presents a solution to this problem by focusing on finding latent mixed…
Topic modeling is one of the most powerful techniques in text mining for data mining, latent data discovery, and finding relationships among data, text documents. Researchers have published many articles in the field of topic modeling and…
The use of hierarchical mixture priors with shared atoms has recently flourished in the Bayesian literature for partially exchangeable data. Leveraging on nested levels of mixtures, these models allow the estimation of a two-layered data…
The role of the microbiome in disease pathogenesis is an emerging field with strong evidence suggesting that dysbiosis is associated with precancerous and cancerous states. Microbiome data present substantial challenges for causal mediation…
Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive…
A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number…
Data allocation plays a critical role in federated large language model (LLM) and small language models (SLMs) reasoning collaboration. Nevertheless, existing data allocation methods fail to address an under-explored challenge in…
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
Dirichlet process mixtures are particularly sensitive to the value of the precision parameter controlling the behavior of the latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to…
The microbiome constitutes a complex microbial ecology of interacting components that regulates important pathways in the host. Measurements of microbial abundances are key to learning the intricate network of interactions amongst microbes.…
In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations,…
Within network data analysis, bipartite networks represent a particular type of network where relationships occur between two disjoint sets of nodes, formally called sending and receiving nodes. In this context, sending nodes may be…
Accurate identification of late-life depression (LLD) using structural brain MRI is essential for monitoring disease progression and facilitating timely intervention. However, existing learning-based approaches for LLD detection are often…
Latent Dirichlet allocation (LDA) is useful in document analysis, image processing, and many information systems; however, its generalization performance has been left unknown because it is a singular learning machine to which regular…
We introduce the problem of learning mixtures of $k$ subcubes over $\{0,1\}^n$, which contains many classic learning theory problems as a special case (and is itself a special case of others). We give a surprising $n^{O(\log k)}$-time…
Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of…
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…