The deep neural network is a widely used framework in machine learning that has been widely applied in various fields. However, deep neural networks often involve a large number of parameters and inputs, many of which may be irrelevant to the goal or true output. These parameters and input variables not only increase computational complexity, but also contribute to additional computational cost. One solution to this problem is knockoff methods, which have proven successful in controlling false discovery rates in high-dimensional regression. Building on the knockoff methods and using the regularised neural network, this paper proposes three variable screening methods under the condition of controlling false discovery rates: one layer filter, multiple layers filter, and variable weight aggregation filter. In comparison with existing algorithms, we find that our algorithms show satisfactory performance.

We study vehicle dispatching in autonomous mobility on demand (AMoD) systems, where a central operator assigns vehicles to customer requests or rejects these with the aim of maximizing its total profit. Recent approaches use multi-agent deep reinforcement learning (MADRL) to realize scalable yet performant algorithms, but train agents based on local rewards, which distorts the reward signal with respect to the system-wide profit, leading to lower performance. We therefore propose a novel global-rewards-based MADRL algorithm for vehicle dispatching in AMoD systems, which resolves so far existing goal conflicts between the trained agents and the operator by assigning rewards to agents leveraging a counterfactual baseline. Our algorithm shows statistically significant improvements across various settings on real-world data compared to state-of-the-art MADRL algorithms with local rewards. We further provide a structural analysis which shows that the utilization of global rewards can improve implicit vehicle balancing and demand forecasting abilities.

In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultra-high dimensional and highly correlated features, in addition to the high noise level. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.

We consider the problem of variable selection in high-dimensional statistical models where the goal is to report a set of variables, out of many predictors $X_1, \dotsc, X_p$, that are relevant to a response of interest. For linear high-dimensional model, where the number of parameters exceeds the number of samples $(p>n)$, we propose a procedure for variables selection and prove that it controls the \emph{directional} false discovery rate (FDR) below a pre-assigned significance level $q\in [0,1]$. We further analyze the statistical power of our framework and show that for designs with subgaussian rows and a common precision matrix $\Omega\in\mathbb{R}^{p\times p}$, if the minimum nonzero parameter $\theta_{\min}$ satisfies $$\sqrt{n} \theta_{\min} - \sigma \sqrt{2(\max_{i\in [p]}\Omega_{ii})\log\left(\frac{2p}{qs_0}\right)} \to \infty\,,$$ then this procedure achieves asymptotic power one. Our framework is built upon the debiasing approach and assumes the standard condition $s_0 = o(\sqrt{n}/(\log p)^2)$, where $s_0$ indicates the number of true positives among the $p$ features. Notably, this framework achieves exact directional FDR control without any assumption on the amplitude of unknown regression parameters, and does not require any knowledge of the distribution of covariates or the noise level. We test our method in synthetic and real data experiments to asses its performance and to corroborate our theoretical results.

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is proposed. Notably, we derive the minimum number of random projections that is sufficient for achieving testing optimality in terms of the minimax rate. An adaptive testing procedure is further established without prior knowledge of regularity. One technical contribution is to establish upper bounds for a range of tail sums of empirical kernel eigenvalues. Simulations and real data analysis are conducted to support our theory.

A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationship of different types. In practice, we do not know what kind of functional relationship is underlying two given observations, Hence the equitability of dependence measure is critical in analysis and by scoring relationships according to an equitable measure one hopes to find important patterns of any type of further examination. In this paper, we introduce our definition of equitability of a dependence measure, which is naturally from this initial description, and Further more power-equitable(weak-equitable) is introduced which is of the most practical meaning in evaluating the equitablity of a dependence measure.

We describe a simple, efficient, permutation based procedure for selecting the penalty parameter in the LASSO. The procedure, which is intended for applications where variable selection is the primary focus, can be applied in a variety of structural settings, including generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of three real data sets in which permutation selection is compared with cross-validation (CV), the Bayesian information criterion (BIC), and a selection method based on recently developed testing procedures for the LASSO.

Reshef & Reshef recently published a paper in which they present a method called the Maximal Information Coefficient (MIC) that can detect all forms of statistical dependence between pairs of variables as sample size goes to infinity. While this method has been praised by some, it has also been criticized for its lack of power in finite samples. We seek to modify MIC so that it has higher power in detecting associations for limited sample sizes. Here we present the Generalized Mean Information Coefficient (GMIC), a generalization of MIC which incorporates a tuning parameter that can be used to modify the complexity of the association favored by the measure. We define GMIC and prove it maintains several key asymptotic properties of MIC. Its increased power over MIC is demonstrated using a simulation of eight different functional relationships at sixty different noise levels. The results are compared to the Pearson correlation, distance correlation, and MIC. Simulation results suggest that while generally GMIC has slightly lower power than the distance correlation measure, it achieves higher power than MIC for many forms of underlying association. For some functional relationships, GMIC surpasses all other statistics calculated. Preliminary results suggest choosing a moderate value of the tuning parameter for GMIC will yield a test that is robust across underlying relationships. GMIC is a promising new method that mitigates the power issues suffered by MIC, at the possible expense of equitability. Nonetheless, distance correlation was in our simulations more powerful for many forms of underlying relationships. At a minimum, this work motivates further consideration of maximal information-based nonparametric exploration (MINE) methods as statistical tests of independence.