Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of observations within the stream to each other via hypothesis testing. Maximum mean discrepancy (MMD; also called energy distance) is a well-known (semi-)metric on the space of probability distributions. MMD gives rise to powerful non-parametric two-sample tests on kernel-enriched domains under mild conditions, which makes its deployment for change detection desirable. However, the classic MMD estimators suffer quadratic complexity, which prohibits their application in the online change detection setting. We propose a general-purpose change detection algorithm, Maximum Mean Discrepancy on Exponential Windows (MMDEW), which leverages the MMD two-sample test, facilitates its efficient online computation on any kernel-enriched domain, and is able to detect any disparity between distributions. Our experiments and analysis show that (1) MMDEW achieves better detection quality than state-of-the-art competitors and that (2) the algorithm has polylogarithmic runtime and logarithmic memory requirements, which allow its deployment to the streaming setting.

Nowadays, gathering high-quality training data from multiple data sources with privacy preservation is a crucial challenge to training high-performance machine learning models. The potential solutions could break the barriers among isolated data corpus, and consequently enlarge the range of data available for processing. To this end, both academic researchers and industrial vendors are recently strongly motivated to propose two main-stream folders of solutions mainly based on software constructions: 1) Secure Multi-party Learning (MPL for short); and 2) Federated Learning (FL for short). The above two technical folders have their advantages and limitations when we evaluate them according to the following five criteria: security, efficiency, data distribution, the accuracy of trained models, and application scenarios. Motivated to demonstrate the research progress and discuss the insights on the future directions, we thoroughly investigate these protocols and frameworks of both MPL and FL. At first, we define the problem of Training machine learning Models over Multiple data sources with Privacy Preservation (TMMPP for short). Then, we compare the recent studies of TMMPP from the aspects of the technical routes, the number of parties supported, data partitioning, threat model, and machine learning models supported, to show their advantages and limitations. Next, we investigate and evaluate five popular FL platforms. Finally, we discuss the potential directions to resolve the problem of TMMPP in the future.

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important challenges: Existing guarantees (1) typically only hold for the averaged iterates rather than the more desirable last iterates, (2) lack convergence metrics that capture the scales of the variables such as Wasserstein distances, and (3) mainly apply to elementary schemes such as stochastic gradient Langevin dynamics. In this paper, we develop a new framework that lifts the above issues by harnessing several tools from the theory of dynamical systems. Our key result is that, for a large class of state-of-the-art sampling schemes, their last-iterate convergence in Wasserstein distances can be reduced to the study of their continuous-time counterparts, which is much better understood. Coupled with standard assumptions of MCMC sampling, our theory immediately yields the last-iterate Wasserstein convergence of many advanced sampling schemes such as proximal, randomized mid-point, and Runge-Kutta integrators. Beyond existing methods, our framework also motivates more efficient schemes that enjoy the same rigorous guarantees.

In the paper, we study a class of nonconvex nonconcave minimax optimization problems (i.e., $\min_x\max_y f(x,y)$), where $f(x,y)$ is possible nonconvex in $x$, and it is nonconcave and satisfies the Polyak-Lojasiewicz (PL) condition in $y$. Moreover, we propose a class of enhanced momentum-based gradient descent ascent methods (i.e., MSGDA and AdaMSGDA) to solve these stochastic Nonconvex-PL minimax problems. In particular, our AdaMSGDA algorithm can use various adaptive learning rates in updating the variables $x$ and $y$ without relying on any global and coordinate-wise adaptive learning rates. Theoretically, we present an effective convergence analysis framework for our methods. Specifically, we prove that our MSGDA and AdaMSGDA methods have the best known sample (gradient) complexity of $O(\epsilon^{-3})$ only requiring one sample at each loop in finding an $\epsilon$-stationary solution (i.e., $\mathbb{E}\|\nabla F(x)\|\leq \epsilon$, where $F(x)=\max_y f(x,y)$). This manuscript commemorates the mathematician Boris Polyak (1935-2023).

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed curves, which often exhibit structural similarities at multiple levels. Modeling multiple closed curves in a way that efficiently incorporates such between-curve dependence remains a challenging problem. In this work, we propose and investigate a multiple-output (a.k.a. multi-output), multi-dimensional Gaussian process modeling framework. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification, on several curve and shape-related tasks. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects in general.

Compression and efficient storage of neural network (NN) parameters is critical for applications that run on resource-constrained devices. Despite the significant progress in NN model compression, there has been considerably less investigation in the actual \textit{physical} storage of NN parameters. Conventionally, model compression and physical storage are decoupled, as digital storage media with error-correcting codes (ECCs) provide robust error-free storage. However, this decoupled approach is inefficient as it ignores the overparameterization present in most NNs and forces the memory device to allocate the same amount of resources to every bit of information regardless of its importance. In this work, we investigate analog memory devices as an alternative to digital media -- one that naturally provides a way to add more protection for significant bits unlike its counterpart, but is noisy and may compromise the stored model's performance if used naively. We develop a variety of robust coding strategies for NN weight storage on analog devices, and propose an approach to jointly optimize model compression and memory resource allocation. We then demonstrate the efficacy of our approach on models trained on MNIST, CIFAR-10 and ImageNet datasets for existing compression techniques. Compared to conventional error-free digital storage, our method reduces the memory footprint by up to one order of magnitude, without significantly compromising the stored model's accuracy.

Stock market forecasting has been a challenging part for many analysts and researchers. Trend analysis, statistical techniques, and movement indicators have traditionally been used to predict stock price movements, but text extraction has emerged as a promising method in recent years. The use of neural networks, especially recurrent neural networks, is abundant in the literature. In most studies, the impact of different users was considered equal or ignored, whereas users can have other effects. In the current study, we will introduce TM-vector and then use this vector to train an IndRNN and ultimately model the market users' behaviour. In the proposed model, TM-vector is simultaneously trained with both the extracted Twitter features and market information. Various factors have been used for the effectiveness of the proposed forecasting approach, including the characteristics of each individual user, their impact on each other, and their impact on the market, to predict market direction more accurately. Dow Jones 30 index has been used in current work. The accuracy obtained for predicting daily stock changes of Apple is based on various models, closed to over 95\% and for the other stocks is significant. Our results indicate the effectiveness of TM-vector in predicting stock market direction.

The Targeted Maximum Likelihood Estimation (TMLE) statistical data analysis framework integrates machine learning, statistical theory, and statistical inference to provide a least biased, efficient and robust strategy for estimation and inference of a variety of statistical and causal parameters. We describe and evaluate the epidemiological applications that have benefited from recent methodological developments. We conducted a systematic literature review in PubMed for articles that applied any form of TMLE in observational studies. We summarised the epidemiological discipline, geographical location, expertise of the authors, and TMLE methods over time. We used the Roadmap of Targeted Learning and Causal Inference to extract key methodological aspects of the publications. We showcase the contributions to the literature of these TMLE results. Of the 81 publications included, 25% originated from the University of California at Berkeley, where the framework was first developed by Professor Mark van der Laan. By the first half of 2022, 70% of the publications originated from outside the United States and explored up to 7 different epidemiological disciplines in 2021-22. Double-robustness, bias reduction and model misspecification were the main motivations that drew researchers towards the TMLE framework. Through time, a wide variety of methodological, tutorial and software-specific articles were cited, owing to the constant growth of methodological developments around TMLE. There is a clear dissemination trend of the TMLE framework to various epidemiological disciplines and to increasing numbers of geographical areas. The availability of R packages, publication of tutorial papers, and involvement of methodological experts in applied publications have contributed to an exponential increase in the number of studies that understood the benefits, and adoption, of TMLE.

We study sequential probability assignment in the Gaussian setting, where the goal is to predict, or equivalently compress, a sequence of real-valued observations almost as well as the best Gaussian distribution with mean constrained to a given subset of $\mathbf{R}^n$. First, in the case of a convex constraint set $K$, we express the hardness of the prediction problem (the minimax regret) in terms of the intrinsic volumes of $K$; specifically, it equals the logarithm of the Wills functional from convex geometry. We then establish a comparison inequality for the Wills functional in the general nonconvex case, which underlines the metric nature of this quantity and generalizes the Slepian-Sudakov-Fernique comparison principle for the Gaussian width. Motivated by this inequality, we characterize the exact order of magnitude of the considered functional for a general nonconvex set, in terms of global covering numbers and local Gaussian widths. This implies metric isomorphic estimates for the log-Laplace transform of the intrinsic volume sequence of a convex body. As part of our analysis, we also characterize the minimax redundancy for a general constraint set. We finally relate and contrast our findings with classical asymptotic results in information theory.

Introduction: The Oncotype DX (ODX) test is a commercially available molecular test for breast cancer assay that provides prognostic and predictive breast cancer recurrence information for hormone positive, HER2-negative patients. The aim of this study is to propose a novel methodology to assist physicians in their decision-making. Methods: A retrospective study between 2012 and 2020 with 333 cases that underwent an ODX assay from three hospitals in Bourgogne Franche-Comt{\'e} was conducted. Clinical and pathological reports were used to collect the data. A methodology based on distributional random forest was developed using 9 clinico-pathological characteristics. This methodology can be used particularly to identify the patients of the training cohort that share similarities with the new patient and to predict an estimate of the distribution of the ODX score. Results: The mean age of participants id 56.9 years old. We have correctly classified 92% of patients in low risk and 40.2% of patients in high risk. The overall accuracy is 79.3%. The proportion of low risk correct predicted value (PPV) is 82%. The percentage of high risk correct predicted value (NPV) is approximately 62.3%. The F1-score and the Area Under Curve (AUC) are of 0.87 and 0.759, respectively. Conclusion: The proposed methodology makes it possible to predict the distribution of the ODX score for a patient and provides an explanation of the predicted score. The use of the methodology with the pathologist's expertise on the different histological and immunohistochemical characteristics has a clinical impact to help oncologist in decision-making regarding breast cancer therapy.