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The current study proposes a dimension reduction method, stepwise support vector machine (SVM), to reduce the dimensions of large p small n datasets. The proposed method is compared with other dimension reduction methods, namely, the…

In this work, we perform a wide variety of experiments with different deep learning architectures on datasets of limited size. According to our study, we show that model complexity is a critical factor when only a few samples per class are…

Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…

Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Parameter-efficient fine-tuning (PEFT) methods such as \lora{} adapt large pretrained models by adding small weight-space updates. While effective, weight deltas are hard to interpret mechanistically, and they do not directly expose…

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

Researchers have been facing a difficult problem that data generation mechanisms could be influenced by internal or external factors leading to the training and test data with quite different distributions, consequently traditional…

Numerical data with bounded domains is a common data type in personal devices, such as wearable sensors. While the collection of such data is essential for third-party platforms, it raises significant privacy concerns. Local differential…

There is an increasing demand to make data "open" to third parties, as data sharing has great benefits in data-driven decision making. However, with a wide variety of sensitive data collected, protecting privacy of individuals, communities…

Representing the 3D environment with instance-aware semantic and geometric information is crucial for interaction-aware robots in dynamic environments. Nevertheless, creating such a representation poses challenges due to sensor noise,…

Machine-learning techniques have become fundamental in high-energy physics and, for new physics searches, it is crucial to know their performance in terms of experimental sensitivity, understood as the statistical significance of the…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…

Feature selection involes identifying the most relevant subset of input features, with a view to improving generalization of predictive models by reducing overfitting. Directly searching for the most relevant combination of attributes is…

Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…

Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem…