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In this paper, we study the convergence of the Adaptive Moment Estimation (Adam) algorithm under unconstrained non-convex smooth stochastic optimizations. Despite the widespread usage in machine learning areas, its theoretical properties remain limited. Prior researches primarily investigated Adam's convergence from an expectation view, often necessitating strong assumptions like uniformly stochastic bounded gradients or problem-dependent knowledge in prior. As a result, the applicability of these findings in practical real-world scenarios has been constrained. To overcome these limitations, we provide a deep analysis and show that Adam could converge to the stationary point in high probability with a rate of $\mathcal{O}\left({\rm poly}(\log T)/\sqrt{T}\right)$ under coordinate-wise "affine" variance noise, not requiring any bounded gradient assumption and any problem-dependent knowledge in prior to tune hyper-parameters. Additionally, it is revealed that Adam confines its gradients' magnitudes within an order of $\mathcal{O}\left({\rm poly}(\log T)\right)$. Finally, we also investigate a simplified version of Adam without one of the corrective terms and obtain a convergence rate that is adaptive to the noise level.

Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates have been established for first order LP algorithms, despite the fact that the underlying formulations are not strongly convex. However, the convergence rate typically depends on the Hoffman constant of a large matrix that contains the constraint matrix, as well as the right hand side, cost, and capacity vectors. We introduce a first order approach for LP optimization with a convergence rate depending polynomially on the circuit imbalance measure, which is a geometric parameter of the constraint matrix, and depending logarithmically on the right hand side, capacity, and cost vectors. This provides much stronger convergence guarantees. For example, if the constraint matrix is totally unimodular, we obtain polynomial-time algorithms, whereas the convergence guarantees for approaches based on primal-dual formulations may have arbitrarily slow convergence rates for this class. Our approach is based on a fast gradient method due to Necoara, Nesterov, and Glineur (Math. Prog. 2019); this algorithm is called repeatedly in a framework that gradually fixes variables to the boundary. This technique is based on a new approximate version of Tardos's method, that was used to obtain a strongly polynomial algorithm for combinatorial LPs (Oper. Res. 1986).

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for Regularized Optimization (SRO). Our SRO algorithm first generates a sketch of the original data matrix, then solves the sketched problem. Different from existing randomized algorithms, our algorithm handles general Frechet subdifferentiable regularization functions in an unified framework. We present general theoretical result for the approximation error between the optimization results of the original problem and the sketched problem for regularized least square problems which can be convex or nonconvex. For arbitrary convex regularizer, relative-error bound is proved for the approximation error. Importantly, minimax rates for sparse signal estimation by solving the sketched sparse convex or nonconvex learning problems are also obtained using our general theoretical result under mild conditions. To the best of our knowledge, our results are among the first to demonstrate minimax rates for convex or nonconvex sparse learning problem by sketching under a unified theoretical framework. We further propose an iterative sketching algorithm which reduces the approximation error exponentially by iteratively invoking the sketching algorithm. Experimental results demonstrate the effectiveness of the proposed SRO and Iterative SRO algorithms.

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are derived based on conjugate priors. We compare the risk functions of direct estimators and Bayesian estimators with respect to different priors that are constructed based on different subsets of observations. We obtain conditions for domination and also prove minimaxity and admissibility in a simple setting.

In this paper we introduce SemiGPC, a distribution-aware label refinement strategy based on Gaussian Processes where the predictions of the model are derived from the labels posterior distribution. Differently from other buffer-based semi-supervised methods such as CoMatch and SimMatch, our SemiGPC includes a normalization term that addresses imbalances in the global data distribution while maintaining local sensitivity. This explicit control allows SemiGPC to be more robust to confirmation bias especially under class imbalance. We show that SemiGPC improves performance when paired with different Semi-Supervised methods such as FixMatch, ReMixMatch, SimMatch and FreeMatch and different pre-training strategies including MSN and Dino. We also show that SemiGPC achieves state of the art results under different degrees of class imbalance on standard CIFAR10-LT/CIFAR100-LT especially in the low data-regime. Using SemiGPC also results in about 2% avg.accuracy increase compared to a new competitive baseline on the more challenging benchmarks SemiAves, SemiCUB, SemiFungi and Semi-iNat.

In this paper, we propose an approach to address the problem of 3D reconstruction of scenes from a single image captured by a light-field camera equipped with a rolling shutter sensor. Our method leverages the 3D information cues present in the light-field and the motion information provided by the rolling shutter effect. We present a generic model for the imaging process of this sensor and a two-stage algorithm that minimizes the re-projection error while considering the position and motion of the camera in a motion-shape bundle adjustment estimation strategy. Thereby, we provide an instantaneous 3D shape-and-pose-and-velocity sensing paradigm. To the best of our knowledge, this is the first study to leverage this type of sensor for this purpose. We also present a new benchmark dataset composed of different light-fields showing rolling shutter effects, which can be used as a common base to improve the evaluation and tracking the progress in the field. We demonstrate the effectiveness and advantages of our approach through several experiments conducted for different scenes and types of motions. The source code and dataset are publicly available at: //github.com/ICB-Vision-AI/RSLF

In this paper, we propose an approach for synthesizing novel view images from a single RGBD (Red Green Blue-Depth) input. Novel view synthesis (NVS) is an interesting computer vision task with extensive applications. Methods using multiple images has been well-studied, exemplary ones include training scene-specific Neural Radiance Fields (NeRF), or leveraging multi-view stereo (MVS) and 3D rendering pipelines. However, both are either computationally intensive or non-generalizable across different scenes, limiting their practical value. Conversely, the depth information embedded in RGBD images unlocks 3D potential from a singular view, simplifying NVS. The widespread availability of compact, affordable stereo cameras, and even LiDARs in contemporary devices like smartphones, makes capturing RGBD images more accessible than ever. In our method, we convert an RGBD image into a point cloud and render it from a different viewpoint, then formulate the NVS task into an image translation problem. We leveraged generative adversarial networks to style-transfer the rendered image, achieving a result similar to a photograph taken from the new perspective. We explore both unsupervised learning using CycleGAN and supervised learning with Pix2Pix, and demonstrate the qualitative results. Our method circumvents the limitations of traditional multi-image techniques, holding significant promise for practical, real-time applications in NVS.

In this paper, we propose a distributed guiding-vector-field (DGVF) algorithm for a team of robots to form a spontaneous-ordering platoon moving along a predefined desired path in the n-dimensional Euclidean space. Particularly, by adding a path parameter as an additional virtual coordinate to each robot, the DGVF algorithm can eliminate the singular points where the vector fields vanish, and govern robots to approach a closed and even self-intersecting desired path. Then, the interactions among neighboring robots and a virtual target robot through their virtual coordinates enable the realization of the desired platoon; in particular, relative parametric displacements can be achieved with arbitrary ordering sequences. Rigorous analysis is provided to guarantee the global convergence to the spontaneous-ordering platoon on the common desired path from any initial positions. 2D experiments using three HUSTER-0.3 unmanned surface vessels (USVs) are conducted to validate the practical effectiveness of the proposed DGVF algorithm, and 3D numerical simulations are presented to demonstrate its effectiveness and robustness when tackling higher-dimensional multi-robot path-navigation missions and some robots breakdown.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.