Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can be applied effectively only when the class of policies being optimized over satisfies strong closure conditions, which is typically not the case when working with parametric policy classes in large-scale environments. In this work, we develop a theoretical framework for PMD for general policy classes where we replace the closure conditions with a strictly weaker variational gradient dominance assumption, and obtain upper bounds on the rate of convergence to the best-in-class policy. Our main result leverages a novel notion of smoothness with respect to a local norm induced by the occupancy measure of the current policy, and casts PMD as a particular instance of smooth non-convex optimization in non-Euclidean space.

Classification with imbalanced data is a common challenge in data analysis, where certain classes (minority classes) account for a small fraction of the training data compared with other classes (majority classes). Classical statistical theory based on large-sample asymptotics and finite-sample corrections is often ineffective for high-dimensional data, leaving many overfitting phenomena in empirical machine learning unexplained. In this paper, we develop a statistical theory for high-dimensional imbalanced classification by investigating support vector machines and logistic regression. We find that dimensionality induces truncation or skewing effects on the logit distribution, which we characterize via a variational problem under high-dimensional asymptotics. In particular, for linearly separable data generated from a two-component Gaussian mixture model, the logits from each class follow a normal distribution $\mathsf{N}(0,1)$ on the testing set, but asymptotically follow a rectified normal distribution $\max\{\kappa, \mathsf{N}(0,1)\}$ on the training set -- which is a pervasive phenomenon we verified on tabular data, image data, and text data. This phenomenon explains why the minority class is more severely affected by overfitting. Further, we show that margin rebalancing, which incorporates class sizes into the loss function, is crucial for mitigating the accuracy drop for the minority class. Our theory also provides insights into the effects of overfitting on calibration and other uncertain quantification measures.

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 efficiently estimating the mean in high dimensions on corrupted data. While several algorithms have been proposed that achieve near-optimal error, they all rely on large data size requirements as a function of dimension. In this paper, we perform an extensive experimentation over various mean estimation techniques where data size might not meet this requirement due to the highdimensional setting. For data with inliers generated from a Gaussian with known covariance, we find experimentally that several robust mean estimation techniques can practically improve upon the sample mean, with the quantum entropy scaling approach from Dong et.al.

The proliferation of data has sparked significant interest in leveraging findings from one study to estimate treatment effects in a different target population without direct outcome observations. However, the transfer learning process is frequently hindered by substantial covariate shift and limited overlap between (i) the source and target populations, as well as (ii) the treatment and control groups within the source. We propose a novel method for overlap-adaptive transfer learning of conditional average treatment effect (CATE) using kernel ridge regression (KRR). Our approach involves partitioning the labeled source data into two subsets. The first one is used to train candidate CATE models based on regression adjustment and pseudo-outcomes. An optimal model is then selected using the second subset and unlabeled target data, employing another pseudo-outcome-based strategy. We provide a theoretical justification for our method through sharp non-asymptotic MSE bounds, highlighting its adaptivity to both weak overlaps and the complexity of CATE function. Extensive numerical studies confirm that our method achieves superior finite-sample efficiency and adaptability. We conclude by demonstrating the effectiveness of our approach using a 401(k) eligibility dataset.

We study the task of Multiclass Linear Classification (MLC) in the distribution-free PAC model with Random Classification Noise (RCN). Specifically, the learner is given a set of labeled examples $(x, y)$, where $x$ is drawn from an unknown distribution on $R^d$ and the labels are generated by a multiclass linear classifier corrupted with RCN. That is, the label $y$ is flipped from $i$ to $j$ with probability $H_{ij}$ according to a known noise matrix $H$ with non-negative separation $\sigma: = \min_{i \neq j} H_{ii}-H_{ij}$. The goal is to compute a hypothesis with small 0-1 error. For the special case of two labels, prior work has given polynomial-time algorithms achieving the optimal error. Surprisingly, little is known about the complexity of this task even for three labels. As our main contribution, we show that the complexity of MLC with RCN becomes drastically different in the presence of three or more labels. Specifically, we prove super-polynomial Statistical Query (SQ) lower bounds for this problem. In more detail, even for three labels and constant separation, we give a super-polynomial lower bound on the complexity of any SQ algorithm achieving optimal error. For a larger number of labels and smaller separation, we show a super-polynomial SQ lower bound even for the weaker goal of achieving any constant factor approximation to the optimal loss or even beating the trivial hypothesis.

The K-Modes algorithm, developed for clustering categorical data, is of high algorithmic simplicity but suffers from unreliable performances in clustering quality and clustering efficiency, both heavily influenced by the choice of initial cluster centers. In this paper, we investigate Bisecting K-Modes (BK-Modes), a successive bisecting process to find clusters, in examining how good the cluster centers out of the bisecting process will be when used as initial centers for the K-Modes. The BK-Modes works by splitting a dataset into multiple clusters iteratively with one cluster being chosen and bisected into two clusters in each iteration. We use the sum of distances of data to their cluster centers as the selection metric to choose a cluster to be bisected in each iteration. This iterative process stops when K clusters are produced. The centers of these K clusters are then used as the initial cluster centers for the K-Modes. Experimental studies of the BK-Modes were carried out and were compared against the K-Modes with multiple sets of initial cluster centers as well as the best of the existing methods we found so far in our survey. Experimental results indicated good performances of BK-Modes both in the clustering quality and efficiency for large datasets.

The rapid emergence of highly adaptable and reusable artificial intelligence (AI) models is set to revolutionize the medical field, particularly in the diagnosis and management of Parkinson's disease (PD). Currently, there are no effective biomarkers for diagnosing PD, assessing its severity, or tracking its progression. Numerous AI algorithms are now being used for PD diagnosis and treatment, capable of performing various classification tasks based on multimodal and heterogeneous disease symptom data, such as gait, hand movements, and speech patterns of PD patients. They provide expressive feedback, including predicting the potential likelihood of PD, assessing the severity of individual or multiple symptoms, aiding in early detection, and evaluating rehabilitation and treatment effectiveness, thereby demonstrating advanced medical diagnostic capabilities. Therefore, this work provides a surveyed compilation of recent works regarding PD detection and assessment through biometric symptom recognition with a focus on machine learning and deep learning approaches, emphasizing their benefits, and exposing their weaknesses, and their impact in opening up newer research avenues. Additionally, it also presents categorized and characterized descriptions of the datasets, approaches, and architectures employed to tackle associated constraints. Furthermore, the paper explores the potential opportunities and challenges presented by data-driven AI technologies in the diagnosis of PD.

Non-rigid alignment of point clouds is crucial for scene understanding, reconstruction, and various computer vision and robotics tasks. Recent advancements in implicit deformation networks for non-rigid registration have significantly reduced the reliance on large amounts of annotated training data. However, existing state-of-the-art methods still face challenges in handling occlusion scenarios. To address this issue, this paper introduces an innovative unsupervised method called Occlusion-Aware Registration (OAR) for non-rigidly aligning point clouds. The key innovation of our method lies in the utilization of the adaptive correntropy function as a localized similarity measure, enabling us to treat individual points distinctly. In contrast to previous approaches that solely minimize overall deviations between two shapes, we combine unsupervised implicit neural representations with the maximum correntropy criterion to optimize the deformation of unoccluded regions. This effectively avoids collapsed, tearing, and other physically implausible results. Moreover, we present a theoretical analysis and establish the relationship between the maximum correntropy criterion and the commonly used Chamfer distance, highlighting that the correntropy-induced metric can be served as a more universal measure for point cloud analysis. Additionally, we introduce locally linear reconstruction to ensure that regions lacking correspondences between shapes still undergo physically natural deformations. Our method achieves superior or competitive performance compared to existing approaches, particularly when dealing with occluded geometries. We also demonstrate the versatility of our method in challenging tasks such as large deformations, shape interpolation, and shape completion under occlusion disturbances. Non-rigid point cloud registration is a critical and challenging problem within the domains of computer vision, robotics, and medical imaging.

Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency regularization term, there is a lack of research on the relationship between them. To address this gap, this paper introduces a more comprehensive mathematical framework for data augmentation. Through this framework, we establish that the expected risk of the shifted population is the sum of the original population risk and a gap term, which can be interpreted as a consistency regularization term. The paper also provides a theoretical understanding of this gap, highlighting its negative effects on the early stages of training. We also propose a method to mitigate these effects. To validate our approach, we conducted experiments using same data augmentation techniques and computing resources under several scenarios, including standard training, out-of-distribution, and imbalanced classification. The results demonstrate that our methods surpass compared methods under all scenarios in terms of generalization ability and convergence stability. We provide our code implementation at the following link: https://github.com/ydlsfhll/ASPR.

Community detection is a cornerstone problem in social network analysis (SNA), aimed at identifying cohesive communities with minimal external links. However, the rise of generative AI and Metaverse introduce complexities by creating hybrid human-AI social networks (denoted by HASNs), where traditional methods fall short, especially in human-centric settings. This paper introduces a novel community detection problem in HASNs (denoted by MetaCD), which seeks to enhance human connectivity within communities while reducing the presence of AI nodes. Effective processing of MetaCD poses challenges due to the delicate trade-off between excluding certain AI nodes and maintaining community structure. To address this, we propose CUSA, an innovative framework incorporating AI-aware clustering techniques that navigate this trade-off by selectively retaining AI nodes that contribute to community integrity. Furthermore, given the scarcity of real-world HASNs, we devise four strategies for synthesizing these networks under various hypothetical scenarios. Empirical evaluations on real social networks, reconfigured as HASNs, demonstrate the effectiveness and practicality of our approach compared to traditional non-deep learning and graph neural network (GNN)-based methods.