Globally Convergent Accelerated Algorithms for Multilinear Sparse Logistic Regression with ℓ0\ell_0-constraints

Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the analysis of multidimensional data. To improve its efficacy and interpretability, we present a Multilinear Sparse Logistic Regression model with $\ell_0$-constraints ($\ell_0$-MLSR). In contrast to the $\ell_1$-norm and $\ell_2$-norm, the $\ell_0$-norm constraint is better suited for feature selection. However, due to its nonconvex and nonsmooth properties, solving it is challenging and convergence guarantees are lacking. Additionally, the multilinear operation in $\ell_0$-MLSR also brings non-convexity. To tackle these challenges, we propose an Accelerated Proximal Alternating Linearized Minimization with Adaptive Momentum (APALM$^+$) method to solve the $\ell_0$-MLSR model. We provide a proof that APALM$^+$ can ensure the convergence of the objective function of $\ell_0$-MLSR. We also demonstrate that APALM$^+$ is globally convergent to a first-order critical point as well as establish convergence rate by using the Kurdyka-Lojasiewicz property. Empirical results obtained from synthetic and real-world datasets validate the superior performance of our algorithm in terms of both accuracy and speed compared to other state-of-the-art methods.Comment: arXiv admin note: text overlap with arXiv:2308.1212

Semiconductor nanowires for future nanoscale application: Synthesis, characterization and nanoelectronic devices

Ph.DDOCTOR OF PHILOSOPH

Spaces to Bloch-type Spaces

Abstract. Let H(B) denote the space of all holomorphic functions on the unit ball B ⊂ C n . Let ϕ be a holomorphic self-map of B and g ∈ H(B). In this paper, we investigate the boundedness and compactness of the Volterra composition operator which map from general function space F (p, q, s) to Bloch-type space B α in the unit ball

Learning to Sit: Synthesizing Human-Chair Interactions via Hierarchical Control

Recent progress on physics-based character animation has shown impressive breakthroughs on human motion synthesis, through imitating motion capture data via deep reinforcement learning. However, results have mostly been demonstrated on imitating a single distinct motion pattern, and do not generalize to interactive tasks that require flexible motion patterns due to varying human-object spatial configurations. To bridge this gap, we focus on one class of interactive tasks -- sitting onto a chair. We propose a hierarchical reinforcement learning framework which relies on a collection of subtask controllers trained to imitate simple, reusable mocap motions, and a meta controller trained to execute the subtasks properly to complete the main task. We experimentally demonstrate the strength of our approach over different non-hierarchical and hierarchical baselines. We also show that our approach can be applied to motion prediction given an image input. A supplementary video can be found at https://youtu.be/3CeN0OGz2cA.Comment: Accepted to AAAI 202

Operation performance test and analysis of 4GQ–1C sugar-cane harvester

4GQ–1C sugarcane harvester was designed to solve current problems that large and mediumsized sugarcane harvesters were in low adaptability in sloping l and, small row spacing and small plots of areas sugarcane harvesting. In order to verify adaptability and reliability of 4GQ–1C sugarcane harvester, field tests were carried out compared with existing models. Results showed that 4GQ–1C sugarcane harvester has good operation performance of lower imp urity rate and loss rate of sugarcane, stronger harvesting adaptability in small row spacing areas and more convenient in collecting sugarcane comparing with sugarcane harvesters with power of 132 and 194 kw. Furthermore, 4GQ–1C sugarcane harvester is compact and flexible with good adaptability and good harvest effect in sugarcane growing area with small and mediumsized planting scale, it is worth popularizing and applying in sugarcane harvest

Regularized Training and Tight Certification for Randomized Smoothed Classifier with Provable Robustness

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient and can be implemented in parallel with other empirical defense methods. We discuss how to implement it under both standard (non-adversarial) and adversarial training scheme. At the same time, we also design a new certification algorithm, which can leverage the regularization effect to provide tighter robustness lower bound that holds with high probability. Our extensive experimentation demonstrates the effectiveness of the proposed training and certification approaches on CIFAR-10 and ImageNet datasets.Comment: AAAI202