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Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the apparent Shannon mutual information (ASI) is; indeed it is the unique prediction quality measure with either of two very different lists of desirable properties, as previously shown by de Finetti and other authors. However, estimating the uncertainty of the ASI is a difficult problem, because of long and non-symmetric heavy tails to the distribution of the individual values of $j(x,y)=\log\frac{Q_y(x)}{P(x)}$ We propose a Bayesian modelling method for the distribution of $j(x,y)$, from the posterior distribution of which the uncertainty in the ASI can be inferred. This method is based on Dirichlet-based mixtures of skew-Student distributions. We illustrate its use on data from a Bayesian model for prediction of the recurrence time of prostate cancer. We believe that this approach is generally appropriate for most problems, where it is infeasible to derive the explicit distribution of the samples of $j(x,y)$, though the precise modelling parameters may need adjustment to suit particular cases.

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy a large number of interactive samples, and the communication between these samples is crucial in speeding up the convergence. To justify the validity of these sampling strategies, the concept of interacting particles naturally calls for the mean-field theory. The theory establishes a correspondence between particle interactions encoded in a set of coupled ODEs/SDEs and a PDE that characterizes the evolution of the underlying distribution. This bridges numerical algorithms with the PDE theory used to show convergence in time. Many mathematical machineries are developed to provide the mean-field analysis, and we showcase two such examples: The coupling method and the compactness argument built upon the martingale strategy. The former has been deployed to show the convergence of ensemble Kalman sampler and ensemble Kalman inversion, and the latter will be shown to be immensely powerful in proving the validity of the Vlasov-Boltzmann simulator.

Model averaging (MA), a technique for combining estimators from a set of candidate models, has attracted increasing attention in machine learning and statistics. In the existing literature, there is an implicit understanding that MA can be viewed as a form of shrinkage estimation that draws the response vector towards the subspaces spanned by the candidate models. This paper explores this perspective by establishing connections between MA and shrinkage in a linear regression setting with multiple nested models. We first demonstrate that the optimal MA estimator is the best linear estimator with monotonically non-increasing weights in a Gaussian sequence model. The Mallows MA (MMA), which estimates weights by minimizing the Mallows' $C_p$ over the unit simplex, can be viewed as a variation of the sum of a set of positive-part Stein estimators. Indeed, the latter estimator differs from the MMA only in that its optimization of Mallows' $C_p$ is within a suitably relaxed weight set. Motivated by these connections, we develop a novel MA procedure based on a blockwise Stein estimation. The resulting Stein-type MA estimator is asymptotically optimal across a broad parameter space when the variance is known. Numerical results support our theoretical findings. The connections established in this paper may open up new avenues for investigating MA from different perspectives. A discussion on some topics for future research concludes the paper.

Backreferences and lookaheads are vital features to make classical regular expressions (REGEX) practical. Although these features have been widely used, understanding of the unrestricted combination of them has been limited. Practically, most likely no implementation fully supports them. Theoretically, while some studies have addressed these features separately, few have dared to combine them. In those few studies, it has been made clear that the amalgamation of these features renders REGEX significantly expressive. However, no acceptable expressivity bound for REWBLk$\unicode{x2014}$REGEX with backreferences and lookaheads$\unicode{x2014}$has been established. We elucidate this by establishing that REWBLk coincides with NLOG, the class of languages accepted by log-space nondeterministic Turing machines (NTMs). In translating REWBLk to log-space NTMs, negative lookaheads are the most challenging part since it essentially requires complementing log-space NTMs in nondeterministic log-space. To address this problem, we revisit Immerman$\unicode{x2013}$Szelepcs\'enyi theorem. In addition, we employ log-space nested-oracles NTMs to naturally handle nested lookaheads of REWBLk. Utilizing such oracle machines, we also present the new result that the membership problem of REWBLk is PSPACE-complete.

Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the remaining ones do not consider scenarios in which the ratio of the number of covariates to sample size is high. In this work, we compare the discrimination performance of lasso and maximum likelihood estimation in logistic regression using simulation studies and applications. Variable selection is done both by lasso and by stepwise when maximum likelihood estimation is used. We consider a wide range of values for the ratio of the number of covariates to sample size. The main conclusion of the work is that lasso has a better discrimination performance than maximum likelihood estimation when the ratio of the number of covariates to sample size is high.

The paper describes how various techniques for applying artificial intelligence to the study of human eyes are utilized. The first dataset was collected using computerized perimetry to investigate the visualization of the human visual field and the diagnosis of glaucoma. A method to analyze the image using software tools is proposed. The second dataset was obtained, as part of the implementation of a Russian-Swiss experiment to collect and analyze eye movement data using the Tobii Pro Glasses 3 device on VR video. Eye movements and focus on the recorded route of a virtual journey through the canton of Vaud were investigated. Methods are being developed to investigate the dependencies of eye pupil movements using mathematical modelling. VR-video users can use these studies in medicine to assess the course and deterioration of glaucoma patients and to study the mechanisms of attention to tourist attractions.

Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.

Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.

Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.