Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized LRMR, a practical setting where the responses and/or the covariates are discretized to finite precision. We focus on the estimation of the underlying coefficient matrix. To make consistent estimator that could achieve arbitrarily small error possible, we employ uniform quantization with random dithering, i.e., we add appropriate random noise to the data before quantization. Specifically, uniform dither and triangular dither are used for responses and covariates, respectively. Based on the quantized data, we propose the constrained Lasso and regularized Lasso estimators, and derive the non-asymptotic error bounds. With the aid of dithering, the estimators achieve minimax optimal rate, while quantization only slightly worsens the multiplicative factor in the error rate. Moreover, we extend our results to a low-rank regression model with matrix responses. We corroborate and demonstrate our theoretical results via simulations on synthetic data or image restoration.

Welcome to the sixth edition of the AI Index Report! This year, the report introduces more original data than any previous edition, including a new chapter on AI public opinion, a more thorough technical performance chapter, original analysis about large language and multimodal models, detailed trends in global AI legislation records, a study of the environmental impact of AI systems, and more. The AI Index Report tracks, collates, distills, and visualizes data related to artificial intelligence. Our mission is to provide unbiased, rigorously vetted, broadly sourced data in order for policymakers, researchers, executives, journalists, and the general public to develop a more thorough and nuanced understanding of the complex field of AI. The report aims to be the world's most credible and authoritative source for data and insights about AI.

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.

The multivariate Hawkes process (MHP) is widely used for analyzing data streams that interact with each other, where events generate new events within their own dimension (via self-excitation) or across different dimensions (via cross-excitation). However, in certain applications, the timestamps of individual events in some dimensions are unobservable, and only event counts within intervals are known, referred to as partially interval-censored data. The MHP is unsuitable for handling such data since its estimation requires event timestamps. In this study, we introduce the Partial Mean Behavior Poisson (PMBP) process, a novel point process which shares parameter equivalence with the MHP and can effectively model both timestamped and interval-censored data. We demonstrate the capabilities of the PMBP process using synthetic and real-world datasets. Firstly, we illustrate that the PMBP process can approximate MHP parameters and recover the spectral radius using synthetic event histories. Next, we assess the performance of the PMBP process in predicting YouTube popularity and find that it surpasses state-of-the-art methods. Lastly, we leverage the PMBP process to gain qualitative insights from a dataset comprising daily COVID-19 case counts from multiple countries and COVID-19-related news articles. By clustering the PMBP-modeled countries, we unveil hidden interaction patterns between occurrences of COVID-19 cases and news reporting.

Simulation studies play a key role in the validation of causal inference methods. The simulation results are reliable only if the study is designed according to the promised operational conditions of the method-in-test. Still, many causal inference literature tend to design over-restricted or misspecified studies. In this paper, we elaborate on the problem of improper simulation design for causal methods and compile a list of desiderata for an effective simulation framework. We then introduce partially randomized causal simulation (PARCS), a simulation framework that meets those desiderata. PARCS synthesizes data based on graphical causal models and a wide range of adjustable parameters. There is a legible mapping from usual causal assumptions to the parameters, thus, users can identify and specify the subset of related parameters and randomize the remaining ones to generate a range of complying data-generating processes for their causal method. The result is a more comprehensive and inclusive empirical investigation for causal claims. Using PARCS, we reproduce and extend the simulation studies of two well-known causal discovery and missing data analysis papers to emphasize the necessity of a proper simulation design. Our results show that those papers would have improved and extended the findings, had they used PARCS for simulation. The framework is implemented as a Python package, too. By discussing the comprehensiveness and transparency of PARCS, we encourage causal inference researchers to utilize it as a standard tool for future works.

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have concurrently made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks, which offers a perspective distinct from prior research. Specifically, we explore the rationale underlying a common practice during the construction of neural network models: sample splitting. Our findings indicate that the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness.

We propose a Universal Defence against backdoor attacks based on Clustering and Centroids Analysis (CCA-UD). The goal of the defence is to reveal whether a Deep Neural Network model is subject to a backdoor attack by inspecting the training dataset. CCA-UD first clusters the samples of the training set by means of density-based clustering. Then, it applies a novel strategy to detect the presence of poisoned clusters. The proposed strategy is based on a general misclassification behaviour observed when the features of a representative example of the analysed cluster are added to benign samples. The capability of inducing a misclassification error is a general characteristic of poisoned samples, hence the proposed defence is attack-agnostic. This marks a significant difference with respect to existing defences, that, either can defend against only some types of backdoor attacks, or are effective only when some conditions on the poisoning ratio or the kind of triggering signal used by the attacker are satisfied. Experiments carried out on several classification tasks and network architectures, considering different types of backdoor attacks (with either clean or corrupted labels), and triggering signals, including both global and local triggering signals, as well as sample-specific and source-specific triggers, reveal that the proposed method is very effective to defend against backdoor attacks in all the cases, always outperforming the state of the art techniques.

Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a simple algorithm performing a weighted average of the prediction of a sample and its nearest neighbors' (computed in latent space) leading to a minor favorable outcomes for a variety of important measures for neural networks. In our evaluation, we employ various self-trained and pre-trained convolutional neural networks to show that our approach improves (i) resistance to label noise, (ii) robustness against adversarial attacks, (iii) classification accuracy, and to some degree even (iv) interpretability. While improvements are not necessarily large in all four areas, our approach is conceptually simple, i.e., improvements come without any modification to network architecture, training procedure or dataset. Furthermore, they are in stark contrast to prior works that often require trade-offs among the four objectives or provide valuable, but non-actionable insights.

In this paper, we address the problem of learning a binary (positive vs. negative) classifier given Positive and Unlabeled data commonly referred to as PU learning. Although rudimentary techniques like clustering, out-of-distribution detection, or positive density estimation can be used to solve the problem in low-dimensional settings, their efficacy progressively deteriorates with higher dimensions due to the increasing complexities in the data distribution. In this paper we propose to learn a neural network-based data representation using a loss function that can be used to project the unlabeled data into two (positive and negative) clusters that can be easily identified using simple clustering techniques, effectively emulating the phenomenon observed in low-dimensional settings. We adopt a vector quantization technique for the learned representations to amplify the separation between the learned unlabeled data clusters. We conduct experiments on simulated PU data that demonstrate the improved performance of our proposed method compared to the current state-of-the-art approaches. We also provide some theoretical justification for our two cluster-based approach and our algorithmic choices.

This literature review aimed to compare various time-series analysis approaches utilized in forecasting COVID-19 cases in Africa. The study involved a methodical search for English-language research papers published between January 2020 and July 2023, focusing specifically on papers that utilized time-series analysis approaches on COVID-19 datasets in Africa. A variety of databases including PubMed, Google Scholar, Scopus, and Web of Science were utilized for this process. The research papers underwent an evaluation process to extract relevant information regarding the implementation and performance of the time-series analysis models. The study highlighted the different methodologies employed, evaluating their effectiveness and limitations in forecasting the spread of the virus. The result of this review could contribute deeper insights into the field, and future research should consider these insights to improve time series analysis models and explore the integration of different approaches for enhanced public health decision-making.