Related papers: A Note on High Dimensional Linear Regression with …

Hierarchical probabilistic models are able to use a large number of parameters to create a model with a high representation power. However, it is well known that increasing the number of parameters also increases the complexity of the model…

This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…

In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…

Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a…

Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…

Selecting interactions from an ultrahigh-dimensional statistical model with $n$ observations and $p$ variables when $p\gg n$ is difficult because the number of candidates for interactions is $p(p-1)/2$ and a selected model should satisfy…

We consider the problem of variable selection in linear models when $p$, the number of potential regressors, may exceed (and perhaps substantially) the sample size $n$ (which is possibly small).

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…

Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…

While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…

The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size,…

High-dimensional biomarkers such as genomics are increasingly being measured in randomized clinical trials. Consequently, there is a growing interest in developing methods that improve the power to detect biomarker-treatment interactions.…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Multi-criteria decision making in large databases is very important in real world applications. Recently, an interactive query has been studied extensively in the database literature with the advantage of both the top-k query (with limited…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Relief based algorithms have often been claimed to uncover feature interactions. However, it is still unclear whether and how interaction terms will be differentiated from marginal effects. In this paper, we propose IMMIGRATE algorithm by…

Following the pivotal success of learning strategies to win at tasks, solely by interacting with an environment without any supervision, agents have gained the ability to make sequential decisions in complex MDPs. Yet, reinforcement…