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This paper revisits the problem of sampling and transmitting status updates through a channel with random delay under a sampling frequency constraint \cite{sun_17_tit}. We use the Age of Information (AoI) to characterize the status information freshness at the receiver. The goal is to design a sampling policy that can minimize the average AoI when the statistics of delay is unknown. We reformulate the problem as the optimization of a renewal-reward process, and propose an online sampling strategy based on the Robbins-Monro algorithm. We prove that the proposed algorithm satisfies the sampling frequency constraint. Moreover, when the transmission delay is bounded and its distribution is absolutely continuous, the average AoI obtained by the proposed algorithm converges to the minimum AoI when the number of samples $K$ goes to infinity with probability 1. We show that the optimality gap decays with rate $\mathcal{O}\left(\ln K/K\right)$, and the proposed algorithm is minimax rate optimal. Simulation results validate the performance of our proposed algorithm.

The number of information systems (IS) studies dealing with explainable artificial intelligence (XAI) is currently exploding as the field demands more transparency about the internal decision logic of machine learning (ML) models. However, most techniques subsumed under XAI provide post-hoc-analytical explanations, which have to be considered with caution as they only use approximations of the underlying ML model. Therefore, our paper investigates a series of intrinsically interpretable ML models and discusses their suitability for the IS community. More specifically, our focus is on advanced extensions of generalized additive models (GAM) in which predictors are modeled independently in a non-linear way to generate shape functions that can capture arbitrary patterns but remain fully interpretable. In our study, we evaluate the prediction qualities of five GAMs as compared to six traditional ML models and assess their visual outputs for model interpretability. On this basis, we investigate their merits and limitations and derive design implications for further improvements.

The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also been suggested for incomplete data. However, the penalty term based on the `complete' sample size $N$ is the same no matter whether in a complete or incomplete data case. For incomplete data, there are often only $N_i<N$ observations for variable $i$, which means that using the `complete' sample size $N$ implausibly ignores the amounts of missing information inherent in incomplete data. Given this observation, a novel criterion called hierarchical BIC (HBIC) for factor analysis with incomplete data is proposed. The novelty is that it only uses the actual amounts of observed information, namely $N_i$'s, in the penalty term. Theoretically, it is shown that HBIC is a large sample approximation of variational Bayesian (VB) lower bound, and BIC is a further approximation of HBIC, which means that HBIC shares the theoretical consistency of BIC. Experiments on synthetic and real data sets are conducted to access the finite sample performance of HBIC, BIC, and related criteria with various missing rates. The results show that HBIC and BIC perform similarly when the missing rate is small, but HBIC is more accurate when the missing rate is not small.

A novel distributed control law for consensus of networked double integrator systems with biased measurements is developed in this article. The agents measure relative positions over a time-varying, undirected graph with an unknown and constant sensor bias corrupting the measurements. An adaptive control law is derived using Lyapunov methods to estimate the individual sensor biases accurately. The proposed algorithm ensures that position consensus is achieved exponentially in addition to bias estimation. The results leverage recent advances in collective initial excitation based results in adaptive estimation. Conditions connecting bipartite graphs and collective initial excitation are also developed. The algorithms are illustrated via simulation studies on a network of double integrators with local communication and biased measurements.

We provide a decision theoretic analysis of bandit experiments. The setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define suitable notions of asymptotic Bayes and minimax risk for bandit experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear second-order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non-parametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit experiment with a PDE which can be efficiently solved using sparse matrix routines. We derive the optimal Bayes and minimax policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such as Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives.

Heavy ball momentum is a popular acceleration idea in stochastic optimization. There have been several attempts to understand its perceived benefits, but the complete picture is still unclear. Specifically, the error expression in the presence of noise has two separate terms: the bias and the variance, but most existing works only focus on bias and show that momentum accelerates its decay. Such analyses overlook the interplay between bias and variance and, therefore, miss important implications. In this work, we analyze a sample complexity bound of stochastic approximation algorithms with heavy-ball momentum that accounts for both bias and variance. We find that for the same step size, which is small enough, the iterates with momentum have improved sample complexity compared to the ones without. However, by using a different step-size sequence, the non-momentum version can nullify this benefit. Subsequently, we show that our sample complexity bounds are indeed tight for a small enough neighborhood around the solution and large enough noise variance. Our analysis also sheds some light on the finite-time behavior of these algorithms. This explains the perceived benefit in the initial phase of momentum-based schemes.

Randomized Maximum Likelihood (RML) is an approximate posterior sampling methodology, widely used in Bayesian inverse problems with complex forward models, particularly in petroleum engineering applications. The procedure involves solving a multi-objective optimization problem, which can be challenging in high-dimensions and when there are constraints on computational costs. We propose a new methodology for tackling the RML optimization problem based on the high-dimensional Bayesian optimization literature. By sharing data between the different objective functions, we are able to implement RML at a greatly reduced computational cost. We demonstrate the benefits of our methodology in comparison with the solutions obtained by alternative optimization methods on a variety of synthetic and real-world problems, including medical and fluid dynamics applications. Furthermore, we show that the samples produced by our method cover well the high-posterior density regions in all of the experiments.

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.

Although Transformers with fully connected self-attentions are powerful to model long-term dependencies, they are struggling to scale to long texts with thousands of words in language modeling. One of the solutions is to equip the model with a recurrence memory. However, existing approaches directly reuse hidden states from the previous segment that encodes contexts in a uni-directional way. As a result, this prohibits the memory to dynamically interact with the current context that provides up-to-date information for token prediction. To remedy this issue, we propose Look-Ahead Memory (LaMemo) that enhances the recurrence memory by incrementally attending to the right-side tokens, and interpolating with the old memory states to maintain long-term information in the history. LaMemo embraces bi-directional attention and segment recurrence with an additional computation overhead only linearly proportional to the memory length. Experiments on widely used language modeling benchmarks demonstrate its superiority over the baselines equipped with different types of memory.

Learning accurate classifiers for novel categories from very few examples, known as few-shot image classification, is a challenging task in statistical machine learning and computer vision. The performance in few-shot classification suffers from the bias in the estimation of classifier parameters; however, an effective underlying bias reduction technique that could alleviate this issue in training few-shot classifiers has been overlooked. In this work, we demonstrate the effectiveness of Firth bias reduction in few-shot classification. Theoretically, Firth bias reduction removes the $O(N^{-1})$ first order term from the small-sample bias of the Maximum Likelihood Estimator. Here we show that the general Firth bias reduction technique simplifies to encouraging uniform class assignment probabilities for multinomial logistic classification, and almost has the same effect in cosine classifiers. We derive an easy-to-implement optimization objective for Firth penalized multinomial logistic and cosine classifiers, which is equivalent to penalizing the cross-entropy loss with a KL-divergence between the uniform label distribution and the predictions. Then, we empirically evaluate that it is consistently effective across the board for few-shot image classification, regardless of (1) the feature representations from different backbones, (2) the number of samples per class, and (3) the number of classes. Finally, we show the robustness of Firth bias reduction, in the case of imbalanced data distribution. Our implementation is available at //github.com/ehsansaleh/firth_bias_reduction