In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement space into a subspace that accommodates the reduced-dimensional dynamics and a complementary static subspace. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. Building on this, we develop an iterative PredVAR algorithm using maximum likelihood and the expectation-maximization (EM) framework. This algorithm alternately updates the estimates of the latent dynamics and optimal oblique projection, yielding dynamic latent variables with rank-ordered predictability and an explicit latent VAR model that is consistent with the outer projection model. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.

In various verification systems, Restricted Boltzmann Machines (RBMs) have demonstrated their efficacy in both front-end and back-end processes. In this work, we propose the use of RBMs to the image clustering tasks. RBMs are trained to convert images into image embeddings. We employ the conventional bottom-up Agglomerative Hierarchical Clustering (AHC) technique. To address the challenge of limited test face image data, we introduce Agglomerative Hierarchical Clustering based Method for Image Clustering using Restricted Boltzmann Machine (AHC-RBM) with two major steps. Initially, a universal RBM model is trained using all available training dataset. Subsequently, we train an adapted RBM model using the data from each test image. Finally, RBM vectors which is the embedding vector is generated by concatenating the visible-to-hidden weight matrices of these adapted models, and the bias vectors. These vectors effectively preserve class-specific information and are utilized in image clustering tasks. Our experimental results, conducted on two benchmark image datasets (MS-Celeb-1M and DeepFashion), demonstrate that our proposed approach surpasses well-known clustering algorithms such as k-means, spectral clustering, and approximate Rank-order.

Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole collection of weighted sum scalarizations at once instead of fixing a particular one in advance. As examples show, this type of scalarization--in contrast to a pure weighted sum scalarization-is also able to detect ``non-convex" parts of the Pareto frontier. Situations are characterized in which different types of rank reversal occur, and it is explained why this might even be useful for analyzing the ranking procedure. The ranking functions are then extended to sets providing unary indicators for set preferences which establishes, for the first time, the link between set optimization methods and set-based multi-objective optimization. A potential application in machine learning is outlined.

This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson's approach to approximating the diagonal of the Hessian, and couple it with several gradient-based methods to give new scaled algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work.

The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of the other one and establish a novel perturbation upper bound for the distance between the two corresponding singular subspaces. It is well-suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds such as Wedin's Theorem. Empowered by this leave-one-out perturbation theory, we provide a deterministic entrywise analysis for the performance of spectral clustering under mixture models. Our analysis leads to an explicit exponential error rate for spectral clustering of sub-Gaussian mixture models. For the mixture of isotropic Gaussians, the rate is optimal under a weaker signal-to-noise condition than that of L{\"o}ffler et al. (2021).

The StochAstic Recursive grAdient algoritHm (SARAH) algorithm is a variance reduced variant of the Stochastic Gradient Descent (SGD) algorithm that needs a gradient of the objective function from time to time. In this paper, we remove the necessity of a full gradient computation. This is achieved by using a randomized reshuffling strategy and aggregating stochastic gradients obtained in each epoch. The aggregated stochastic gradients serve as an estimate of a full gradient in the SARAH algorithm. We provide a theoretical analysis of the proposed approach and conclude the paper with numerical experiments that demonstrate the efficiency of this approach.

Recent years have seen rapid development in Information Extraction, as well as its subtask, Relation Extraction. Relation Extraction is able to detect semantic relations between entities in sentences. Currently, many efficient approaches have been applied to relation extraction tasks. Supervised learning approaches especially have good performance. However, there are still many difficult challenges. One of the most serious problems is that manually labeled data is difficult to acquire. In most cases, limited data for supervised approaches equals lousy performance. Thus here, under the situation with only limited training data, we focus on how to improve the performance of our supervised baseline system with unsupervised pre-training. Feature is one of the key components in improving the supervised approaches. Traditional approaches usually apply hand-crafted features, which require expert knowledge and expensive human labor. However, this type of feature might suffer from data sparsity: when the training set size is small, the model parameters might be poorly estimated. In this thesis, we present several novel unsupervised pre-training models to learn the distributed text representation features, which are encoded with rich syntactic-semantic patterns of relation expressions. The experiments have demonstrated that this type of feature, combine with the traditional hand-crafted features, could improve the performance of the logistic classification model for relation extraction, especially on the classification of relations with only minor training instances.

Artificial intelligence (AI) has acquired notorious relevance in modern computing as it effectively solves complex tasks traditionally done by humans. AI provides methods to represent and infer knowledge, efficiently manipulate texts and learn from vast amount of data. These characteristics are applicable in many activities that human find laborious or repetitive, as is the case of the analysis of scientific literature. Manually preparing and writing a systematic literature review (SLR) takes considerable time and effort, since it requires planning a strategy, conducting the literature search and analysis, and reporting the findings. Depending on the area under study, the number of papers retrieved can be of hundreds or thousands, meaning that filtering those relevant ones and extracting the key information becomes a costly and error-prone process. However, some of the involved tasks are repetitive and, therefore, subject to automation by means of AI. In this paper, we present a survey of AI techniques proposed in the last 15 years to help researchers conduct systematic analyses of scientific literature. We describe the tasks currently supported, the types of algorithms applied, and available tools proposed in 34 primary studies. This survey also provides a historical perspective of the evolution of the field and the role that humans can play in an increasingly automated SLR process.

We study the compatibility between the optimal statistical parity solutions and individual fairness. While individual fairness seeks to treat similar individuals similarly, optimal statistical parity aims to provide similar treatment to individuals who share relative similarity within their respective sensitive groups. The two fairness perspectives, while both desirable from a fairness perspective, often come into conflict in applications. Our goal in this work is to analyze the existence of this conflict and its potential solution. In particular, we establish sufficient (sharp) conditions for the compatibility between the optimal (post-processing) statistical parity $L^2$ learning and the ($K$-Lipschitz or $(\epsilon,\delta)$) individual fairness requirements. Furthermore, when there exists a conflict between the two, we first relax the former to the Pareto frontier (or equivalently the optimal trade-off) between $L^2$ error and statistical disparity, and then analyze the compatibility between the frontier and the individual fairness requirements. Our analysis identifies regions along the Pareto frontier that satisfy individual fairness requirements. (Lastly, we provide individual fairness guarantees for the composition of a trained model and the optimal post-processing step so that one can determine the compatibility of the post-processed model.) This provides practitioners with a valuable approach to attain Pareto optimality for statistical parity while adhering to the constraints of individual fairness.

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index.