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To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests is available, each test has its strengths but also its blind spots. In a Gaussian sequence model, we study whether it is possible to obtain a test with substantially better consistency properties than the likelihood ratio (i.e., Euclidean norm based) test. We establish an impossibility result, showing that in the high-dimensional framework we consider, the set of alternatives for which a test may improve upon the likelihood ratio test -- that is, its superconsistency points -- is always asymptotically negligible in a relative volume sense.

With increasing interest in procedural content generation by academia and game developers alike, it is vital that different approaches can be compared fairly. However, evaluating procedurally generated video game levels is often difficult, due to the lack of standardised, game-independent metrics. In this paper, we introduce two simulation-based evaluation metrics that involve analysing the behaviour of an A* agent to measure the diversity and difficulty of generated levels in a general, game-independent manner. Diversity is calculated by comparing action trajectories from different levels using the edit distance, and difficulty is measured as how much exploration and expansion of the A* search tree is necessary before the agent can solve the level. We demonstrate that our diversity metric is more robust to changes in level size and representation than current methods and additionally measures factors that directly affect playability, instead of focusing on visual information. The difficulty metric shows promise, as it correlates with existing estimates of difficulty in one of the tested domains, but it does face some challenges in the other domain. Finally, to promote reproducibility, we publicly release our evaluation framework.

Language carries implicit human biases, functioning both as a reflection and a perpetuation of stereotypes that people carry with them. Recently, ML-based NLP methods such as word embeddings have been shown to learn such language biases with striking accuracy. This capability of word embeddings has been successfully exploited as a tool to quantify and study human biases. However, previous studies only consider a predefined set of biased concepts to attest (e.g., whether gender is more or less associated with particular jobs), or just discover biased words without helping to understand their meaning at the conceptual level. As such, these approaches can be either unable to find biased concepts that have not been defined in advance, or the biases they find are difficult to interpret and study. This could make existing approaches unsuitable to discover and interpret biases in online communities, as such communities may carry different biases than those in mainstream culture. This paper improves upon, extends, and evaluates our previous data-driven method to automatically discover and help interpret biased concepts encoded in word embeddings. We apply this approach to study the biased concepts present in the language used in online communities and experimentally show the validity and stability of our method

Federated Learning (FL) has emerged as a result of data ownership and privacy concerns to prevent data from being shared between multiple parties included in a training procedure. Although issues, such as privacy, have gained significant attention in this domain, not much attention has been given to satisfying statistical fairness measures in the FL setting. With this goal in mind, we conduct studies to show that FL is able to satisfy different fairness metrics under different data regimes consisting of different types of clients. More specifically, uncooperative or adversarial clients might contaminate the global FL model by injecting biased or poisoned models due to existing biases in their training datasets. Those biases might be a result of imbalanced training set (Zhang and Zhou 2019), historical biases (Mehrabi et al. 2021a), or poisoned data-points from data poisoning attacks against fairness (Mehrabi et al. 2021b; Solans, Biggio, and Castillo 2020). Thus, we propose a new FL framework that is able to satisfy multiple objectives including various statistical fairness metrics. Through experimentation, we then show the effectiveness of this method comparing it with various baselines, its ability in satisfying different objectives collectively and individually, and its ability in identifying uncooperative or adversarial clients and down-weighing their effect

Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax lower bounds for estimating the underlying low-rank matrix are established allowing a whole range of sample sizes and signal strength. Under a minimal condition on signal strength, referred to as the information-theoretical limit or statistical limit, we prove the minimax optimality of a maximum likelihood estimator which, in general, is computationally infeasible. If the signal is stronger than a certain threshold, called the computational limit, we design a computationally fast estimator based on spectral aggregation and demonstrate its minimax optimality. Moreover, when the signal strength is smaller than the computational limit, we provide evidences based on the low-degree likelihood ratio framework to claim that no polynomial-time algorithm can consistently recover the underlying low-rank matrix. Our results reveal multiple phase transitions in the minimax error rates and the statistical-to-computational gap. Numerical experiments confirm our theoretical findings. We further showcase the merit of our spectral aggregation method on the worldwide food trading dataset.

The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been modified to incorporate this flow and still be well-posed. Herein we first develop some basic properties of the modified model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and proven to be effective.

This paper introduces an integrated lot sizing and scheduling problem inspired from a real-world application in off-the-road tire industry. This problem considers the assignment of different items on parallel machines with complex eligibility constraints within a finite planning horizon. It also considers a large panel of specific constraints such as: backordering, a limited number of setups, upstream resources saturation and customers prioritization. A novel mixed integer formulation is proposed with the objective of optimizing different normalized criteria related to the inventory and service level performance. Based on this mathematical formulation, a problem-based matheuristic method that solves the lot sizing and assignment problems separately is proposed to solve the industrial case. A computational study and sensitivity analysis are carried out based on real-world data with up to 170 products, 70 unrelated parallel machines and 42 periods. The obtained results show the effectiveness of the proposed approach on improving the company's solution. Indeed, the two most important KPIs for the management have been optimized of respectively 32% for the backorders and 13% for the overstock. Moreover, the computational time have been reduced significantly.

In countries where population census and sample survey data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often assume the survey design is ignorable, which may be inappropriate given the complex design of household surveys typically used in this context. On the other hand, small area estimation approaches common in the survey statistics literature do not incorporate both unit-level covariate information and spatial smoothing in a design-consistent way. We propose a new smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing, bridging the survey statistics and model-based geostatistics perspectives. Under certain assumptions, the new estimator can be viewed as both design-consistent and model-consistent, offering potential benefits from both perspectives. We demonstrate our estimator's performance using both real and simulated data, comparing it with existing design-based and model-based estimators.

Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used directly for maximum likelihood estimation. In the stationary case, an approximation using Fourier series has been suggested, but it is limited to rectangular observation windows and no theoretical results support it. In this contribution, we investigate a different way to approximate the likelihood by looking at its asymptotic behaviour when the observation window grows towards $\mathbb{R}^d$. This new approximation is not limited to rectangular windows, is faster to compute than the previous one, does not require any tuning parameter, and some theoretical justifications are provided. It moreover provides an explicit formula for estimating the asymptotic variance of the associated estimator. The performances are assessed in a simulation study on standard parametric models on $\mathbb{R}^d$ and compare favourably to common alternative estimation methods for continuous DPPs.

We study the offline meta-reinforcement learning (OMRL) problem, a paradigm which enables reinforcement learning (RL) algorithms to quickly adapt to unseen tasks without any interactions with the environments, making RL truly practical in many real-world applications. This problem is still not fully understood, for which two major challenges need to be addressed. First, offline RL usually suffers from bootstrapping errors of out-of-distribution state-actions which leads to divergence of value functions. Second, meta-RL requires efficient and robust task inference learned jointly with control policy. In this work, we enforce behavior regularization on learned policy as a general approach to offline RL, combined with a deterministic context encoder for efficient task inference. We propose a novel negative-power distance metric on bounded context embedding space, whose gradients propagation is detached from the Bellman backup. We provide analysis and insight showing that some simple design choices can yield substantial improvements over recent approaches involving meta-RL and distance metric learning. To the best of our knowledge, our method is the first model-free and end-to-end OMRL algorithm, which is computationally efficient and demonstrated to outperform prior algorithms on several meta-RL benchmarks.