Minimax Regret Learning for Data with Heterogeneous Subgroups

Modern complex datasets often consist of various sub-populations. To develop robust and generalizable methods in the presence of sub-population heterogeneity, it is important to guarantee a uniform learning performance instead of an average one. In many applications, prior information is often available on which sub-population or group the data points belong to. Given the observed groups of data, we develop a min-max-regret (MMR) learning framework for general supervised learning, which targets to minimize the worst-group regret. Motivated from the regret-based decision theoretic framework, the proposed MMR is distinguished from the value-based or risk-based robust learning methods in the existing literature. The regret criterion features several robustness and invariance properties simultaneously. In terms of generalizability, we develop the theoretical guarantee for the worst-case regret over a super-population of the meta data, which incorporates the observed sub-populations, their mixtures, as well as other unseen sub-populations that could be approximated by the observed ones. We demonstrate the effectiveness of our method through extensive simulation studies and an application to kidney transplantation data from hundreds of transplant centers.

Low-Rank Online Dynamic Assortment with Dual Contextual Information

As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to optimize assortments over time. In this paper, we consider the dynamic assortment problem with dual contexts -- user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a new low-rank dynamic assortment model to transform this problem into a manageable scale. Then we propose an efficient algorithm that estimates the intrinsic subspaces and utilizes the upper confidence bound approach to address the exploration-exploitation trade-off in online decision making. Theoretically, we establish a regret bound of $\tilde{O}((d_1+d_2)r\sqrt{T})$, where $d_1, d_2$ represent the dimensions of the user and item features respectively, $r$ is the rank of the parameter matrix, and $T$ denotes the time horizon. This bound represents a substantial improvement over prior literature, made possible by leveraging the low-rank structure. Extensive simulations and an application to the Expedia hotel recommendation dataset further demonstrate the advantages of our proposed method.

Mutual-Learning Knowledge Distillation for Nighttime UAV Tracking

Nighttime unmanned aerial vehicle (UAV) tracking has been facilitated with indispensable plug-and-play low-light enhancers. However, the introduction of low-light enhancers increases the extra computational burden for the UAV, significantly hindering the development of real-time UAV applications. Meanwhile, these state-of-the-art (SOTA) enhancers lack tight coupling with the advanced daytime UAV tracking approach. To solve the above issues, this work proposes a novel mutual-learning knowledge distillation framework for nighttime UAV tracking, i.e., MLKD. This framework is constructed to learn a compact and fast nighttime tracker via knowledge transferring from the teacher and knowledge sharing among various students. Specifically, an advanced teacher based on a SOTA enhancer and a superior tracking backbone is adopted for guiding the student based only on the tight coupling-aware tracking backbone to directly extract nighttime object features. To address the biased learning of a single student, diverse lightweight students with different distillation methods are constructed to focus on various aspects of the teacher's knowledge. Moreover, an innovative mutual-learning room is designed to elect the superior student candidate to assist the remaining students frame-by-frame in the training phase. Furthermore, the final best student, i.e., MLKD-Track, is selected through the testing dataset. Extensive experiments demonstrate the effectiveness and superiority of MLKD and MLKD-Track. The practicality of the MLKD-Track is verified in real-world tests with different challenging situations. The code is available at https://github.com/lyfeng001/MLKD.

Consistency of Lloyd's Algorithm Under Perturbations

In the context of unsupervised learning, Lloyd's algorithm is one of the most widely used clustering algorithms. It has inspired a plethora of work investigating the correctness of the algorithm under various settings with ground truth clusters. In particular, in 2016, Lu and Zhou have shown that the mis-clustering rate of Lloyd's algorithm on $n$ independent samples from a sub-Gaussian mixture is exponentially bounded after $O(\log(n))$ iterations, assuming proper initialization of the algorithm. However, in many applications, the true samples are unobserved and need to be learned from the data via pre-processing pipelines such as spectral methods on appropriate data matrices. We show that the mis-clustering rate of Lloyd's algorithm on perturbed samples from a sub-Gaussian mixture is also exponentially bounded after $O(\log(n))$ iterations under the assumptions of proper initialization and that the perturbation is small relative to the sub-Gaussian noise. In canonical settings with ground truth clusters, we derive bounds for algorithms such as $k$-means$++$ to find good initializations and thus leading to the correctness of clustering via the main result. We show the implications of the results for pipelines measuring the statistical significance of derived clusters from data such as SigClust. We use these general results to derive implications in providing theoretical guarantees on the misclustering rate for Lloyd's algorithm in a host of applications, including high-dimensional time series, multi-dimensional scaling, and community detection for sparse networks via spectral clustering.

A Scalable Arrangement Method for Aperiodic Array Antennas to Reduce Peak Sidelobe Level

Peak sidelobe level reduction (PSLR) is crucial in the application of large-scale array antenna, which directly determines the radiation performance of array antenna. We study the PSLR of subarray level aperiodic arrays and propose three array structures: dislocated subarrays with uniform elements (DSUE), uniform subarrays with random elements (USRE), dislocated subarrays with random elements (DSRE). To optimize the dislocation position of subarrays and random position of elements, the improved Bat algorithm (IBA) is applied. To draw the comparison of PSLR effect among these three array structures, we take three size of array antennas from small to large as examples to simulate and calculate the redundancy and peak sidelobe level (PSLL) of them. The results show that DSRE is the optimal array structure by analyzing the dislocation distance of subarray, scanning angle and applicable frequency. The proposed design method is a universal and scalable method, which is of great application value to the design of large-scale aperiodic array antenna.

Asymptotic Inference for Multi-Stage Stationary Treatment Policy with High Dimensional Features

Dynamic treatment rules or policies are a sequence of decision functions over multiple stages that are tailored to individual features. One important class of treatment policies for practice, namely multi-stage stationary treatment policies, prescribe treatment assignment probabilities using the same decision function over stages, where the decision is based on the same set of features consisting of both baseline variables (e.g., demographics) and time-evolving variables (e.g., routinely collected disease biomarkers). Although there has been extensive literature to construct valid inference for the value function associated with the dynamic treatment policies, little work has been done for the policies themselves, especially in the presence of high dimensional feature variables. We aim to fill in the gap in this work. Specifically, we first estimate the multistage stationary treatment policy based on an augmented inverse probability weighted estimator for the value function to increase the asymptotic efficiency, and further apply a penalty to select important feature variables. We then construct one-step improvement of the policy parameter estimators. Theoretically, we show that the improved estimators are asymptotically normal, even if nuisance parameters are estimated at a slow convergence rate and the dimension of the feature variables increases exponentially with the sample size. Our numerical studies demonstrate that the proposed method has satisfactory performance in small samples, and that the performance can be improved with a choice of the augmentation term that approximates the rewards or minimizes the variance of the value function.

Edge-based Monocular Thermal-Inertial Odometry in Visually Degraded Environments

State estimation in complex illumination environments based on conventional visual-inertial odometry is a challenging task due to the severe visual degradation of the visual camera. The thermal infrared camera is capable of all-day time and is less affected by illumination variation. However, most existing visual data association algorithms are incompatible because the thermal infrared data contains large noise and low contrast. Motivated by the phenomenon that thermal radiation varies most significantly at the edges of objects, the study proposes an ETIO, which is the first edge-based monocular thermal-inertial odometry for robust localization in visually degraded environments. Instead of the raw image, we utilize the binarized image from edge extraction for pose estimation to overcome the poor thermal infrared image quality. Then, an adaptive feature tracking strategy ADT-KLT is developed for robust data association based on limited edge information and its distance distribution. Finally, a pose graph optimization performs real-time estimation over a sliding window of recent states by combining IMU pre-integration with reprojection error of all edge feature observations. We evaluated the performance of the proposed system on public datasets and real-world experiments and compared it against state-of-the-art methods. The proposed ETIO was verified with the ability to enable accurate and robust localization all-day time.

MobRecon: Mobile-Friendly Hand Mesh Reconstruction from Monocular Image

In this work, we propose a framework for single-view hand mesh reconstruction, which can simultaneously achieve high reconstruction accuracy, fast inference speed, and temporal coherence. Specifically, for 2D encoding, we propose lightweight yet effective stacked structures. Regarding 3D decoding, we provide an efficient graph operator, namely depth-separable spiral convolution. Moreover, we present a novel feature lifting module for bridging the gap between 2D and 3D representations. This module starts with a map-based position regression (MapReg) block to integrate the merits of both heatmap encoding and position regression paradigms to improve 2D accuracy and temporal coherence. Furthermore, MapReg is followed by pose pooling and pose-to-vertex lifting approaches, which transform 2D pose encodings to semantic features of 3D vertices. Overall, our hand reconstruction framework, called MobRecon, comprises affordable computational costs and miniature model size, which reaches a high inference speed of 83FPS on Apple A14 CPU. Extensive experiments on popular datasets such as FreiHAND, RHD, and HO3Dv2 demonstrate that our MobRecon achieves superior performance on reconstruction accuracy and temporal coherence. Our code is publicly available at https://github.com/SeanChenxy/HandMesh.

Rejoinder: Learning Optimal Distributionally Robust Individualized Treatment Rules

We thank the opportunity offered by editors for this discussion and the discussants for their insightful comments and thoughtful contributions. We also want to congratulate Kallus (2020) for his inspiring work in improving the efficiency of policy learning by retargeting. Motivated from the discussion in Dukes and Vansteelandt (2020), we first point out interesting connections and distinctions between our work and Kallus (2020) in Section 1. In particular, the assumptions and sources of variation for consideration in these two papers lead to different research problems with different scopes and focuses. In Section 2, following the discussions in Li et al. (2020); Liang and Zhao (2020), we also consider the efficient policy evaluation problem when we have some data from the testing distribution available at the training stage. We show that under the assumption that the sample sizes from training and testing are growing in the same order, efficient value function estimates can deliver competitive performance. We further show some connections of these estimates with existing literature. However, when the growth of testing sample size available for training is in a slower order, efficient value function estimates may not perform well anymore. In contrast, the requirement of the testing sample size for DRITR is not as strong as that of efficient policy evaluation using the combined data. Finally, we highlight the general applicability and usefulness of DRITR in Section 3.

Efficient Learning of Optimal Individualized Treatment Rules for Heteroscedastic or Misspecified Treatment-Free Effect Models

Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment-free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estimate can be consistent but may suffer from downgraded efficiency. Other than potential misspecified nuisance models, most existing methods do not account for the potential problem when the variance of outcome is heterogeneous among covariates and treatment. We observe that such heteroscedasticity can greatly affect the estimation efficiency of the optimal ITR. In this paper, we demonstrate that the consequences of misspecified treatment-free effect and heteroscedasticity can be unified as a covariate-treatment dependent variance of residuals. To improve efficiency of the estimated ITR, we propose an Efficient Learning (E-Learning) framework for finding an optimal ITR in the multi-armed treatment setting. We show that the proposed E-Learning is optimal among a regular class of semiparametric estimates that can allow treatment-free effect misspecification. In our simulation study, E-Learning demonstrates its effectiveness if one of or both misspecified treatment-free effect and heteroscedasticity exist. Our analysis of a Type 2 Diabetes Mellitus (T2DM) observational study also suggests the improved efficiency of E-Learning.