Nonparametric Perspective of Deep Learning

Decision of the model complexity is a significant challenge in contemporary data-driven modeling applications. Designing neural architecture involves the process of determining the optimal model complexity for deep neural networks (DNNs) models in order to uncover relationships in real-world data patterns. Consequently, optimizing DNN architectures is crucial for enhancing the practical approximation performance of DNN models to real-world data. This study implements a data-driven neuroevolution scheme for the optimal neural architecture search (NAS) and demonstrates a data-driven engineering application for cooling load estimation. The proposed neuroevolution scheme aims at evolving to the best generalizing DNN model that well suits the modeling complexity requirements of the dataset. To this end, the objective function for the neural architecture optimization process is simplified to the mean square error of the test dataset, which enables to reduce the risk of insufficient generalization during NAS. By employing this objective function for evolution field optimization (EFO), the proposed neuroevolution process can automatically achieve the optimal model complexity, preventing overfitting and underfitting cases, and thereby attaining almost the best generalization for the dataset. For this purpose, this approach combines parametric learning with the backpropagation algorithm and structural learning with EFO-based neural architecture search to address data-driven, optimal complexity DNN model generation problems. Effectiveness of the method is demonstrated in the cooling load estimation problem of residential buildings, and performances of the optimal DNN models with four objective functions are analyzed. The design of objective function for the best generalizing model is also elaborated.

Recent work concerning adversarial attacks on ReLU neural networks has shown that unbounded regions and regions with a sufficiently large volume can be prone to containing adversarial samples. Finding the representation of linear regions and identifying their properties are challenging tasks. In practice, one works with deep neural networks and high-dimensional input data that leads to polytopes represented by an extensive number of inequalities, and hence demanding high computational resources. The approach should be scalable, feasible and numerically stable. We discuss an algorithm that finds the H-representation of each region of a neural network and identifies if the region is bounded or not.KeywordsNeural networkUnbounded polytopeLinear programmingReLU activation function

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article compares and contrasts members from a general class of regularization techniques, which notably includes ridge regression and principal component regression. We derive an explicit finite-sample risk bound for regularization-based estimators that simultaneously accounts for (i) the structure of the ambient function space, (ii) the regularity of the true regression function, and (iii) the adaptability (or qualification) of the regularization. A simple consequence of this upper bound is that the risk of the regularization-based estimators matches the minimax rate in a variety of settings. The general bound also illustrates how some regularization techniques are more adaptable than others to favorable regularity properties that the true regression function may possess. This, in particular, demonstrates a striking difference between kernel ridge regression and kernel principal component regression. Our theoretical results are supported by numerical experiments.

The usage of Deep Neural Networks (DNN) on resource-constrained edge devices has been limited due to their high computation and large memory requirement. In this work, we propose an algorithm to compress DNNs by jointly optimizing structured sparsity and quantization constraints in a single DNN training framework. The proposed algorithm has been extensively validated on high/low capacity DNNs and wide/deep sparse DNNs. Further, we perform Pareto-optimal analysis to extract optimal DNN models from a large set of trained DNN models. The optimal structurally-compressed DNN model achieves ~50X weight memory reduction without test accuracy degradation, compared to floating-point uncompressed DNN.

Although the Deep Neural Network (DNN) technique has been widely applied in various applications, the DNN-based applications are still too computationally intensive for the resource-constrained mobile devices. Many works have been proposed to optimize the DNN computation performance, but most of them are limited in an algorithmic perspective, ignoring certain computing issues in practical deployment. To achieve the comprehensive DNN performance enhancement in practice, the expected DNN optimization works should closely cooperate with specific hardware and system constraints (i.e. computation capacity, energy cost, memory occupancy, and inference latency). Therefore, in this work, we propose ReForm -- a resource-aware DNN optimization framework. Through thorough mobile DNN computing analysis and innovative model reconfiguration schemes (i.e. ADMM based static model fine-tuning, dynamically selective computing), ReForm can efficiently and effectively reconfigure a pre-trained DNN model for practical mobile deployment with regards to various static and dynamic computation resource constraints. Experiments show that ReForm has ~3.5× faster optimization speed than state-of-the-art resource-aware optimization method. Also, ReForm can effective reconfigure a DNN model to different mobile devices with distinct resource constraints. Moreover, ReForm achieves satisfying computation cost reduction with ignorable accuracy drop in both static and dynamic computing scenarios (at most 18% workload, 16.23% latency, 48.63% memory, and 21.5% energy enhancement).

Deep neural network (DNN) models are increasingly popular in edge video analytic applications. However, the computeintensive nature of DNN models pose challenges for energyefficient inference on resource-constrained edge devices. Most existing solutions focus on optimizing DNN inference latency and accuracy, often overlooking energy efficiency. They also fail to account for the varying complexity of video frames, leading to sub-optimal performance in edge video analytics. In this paper, we propose an EnergyEfficient Early-Exit (E4) framework that enhances DNN inference efficiency for edge video analytics by integrating a novel early-exit mechanism with dynamic voltage and frequency scaling (DVFS) governors. It employs an attentionbased cascade module to analyze video frame diversity and automatically determine optimal DNN exit points. Additionally, E4 features a just-in-time (JIT) profiler that uses coordinate descent search to co-optimize CPU and GPU clock frequencies for each layer before the DNN exit points. Extensive evaluations demonstrate that E4 outperforms current state-of-the-art methods, achieving up to 2.8× speedup and 26% average energy saving while maintaining high accuracy.

Deep Neural Networks (DNNs) have gained widespread popularity in different domain applications due to their dominant performance. Despite the prevalence of massively parallel multi-core processor architectures, adopting large DNN models in embedded systems remains challenging, as most embedded applications are designed with single-core processors in mind. This limits DNN adoption in embedded systems due to inefficient leveraging of model parallelization and workload partitioning. Prior solutions attempt to address these challenges using data and model parallelism. However, they lack in finding optimal DNN model partitions and distributing them efficiently to achieve improved performance.This paper proposes a DNN model parallelism framework to accelerate model training by finding the optimal number of model partitions and resource provisions. The proposed framework combines data and model parallelism techniques to optimize the parallel processing of DNNs for embedded applications. In addition, it implements the pipeline execution of the partitioned models and integrates a task controller to manage the computing resources. The experimental results for image object detection demonstrate the applicability of our proposed framework in estimating the latest execution time and reducing overall model training time by almost 44.87% compared to the baseline AlexNet convolutional neural network (CNN) model.

Kernel Ridge Regression combines the principles of machine learning supervision and ridge regression by employing the kernel trick. This approach is particularly effective for regression problems with non-linear relationships between inputs and outputs. The kernel trick allows Kernel Ridge Regression (KRR) to perform ridge regression by learning non-linear functions in a high-dimensional space using ridge regression's regularization techniques. The success of KRR depends on the hyper-parameter settings, which determine the type of kernel used. Current methods for determining hyper-parameter values encounter three primary challenges: high computational costs, large memory demands, and low accuracy. This research introduces a significant improvement to the golden eagle optimization framework by incorporating elite opposite-based learning (EOBL) to enhance population diversity in the search space. We apply this strategy to efficiently select optimal hyper-parameters. Combining EOBL with KRR can lead to improved predictive accuracy. By selecting elite solutions and incorporating opposition-based methodologies, the model can circumvent local optima and broaden the range of potential solutions, leading to improved results, especially in complex datasets. The proposed enhancement to Kernel Ridge Regression was evaluated on ten publicly available multi-class datasets to demonstrate its effectiveness. The results from various evaluation criteria showed that the proposed enhancement achieved superior classification performance compared to all baseline techniques.

In this paper, we consider nonlinear partial integro-differential equations (PIDEs) with gradient-independent Lipschitz continuous nonlinearities and prove that deep neural networks with ReLU activation function can approximate solutions of such semilinear PIDEs without curse of dimensionality in the sense that the required number of parameters in the deep neural networks increases at most polynomially in both the dimension [Formula: see text] of the corresponding PIDE and the reciprocal of the prescribed accuracy [Formula: see text].

Generalization error of random feature and kernel methods: Hypercontractivity and kernel matrix concentration

Deep neural networks(DNN) are being extensively used in the field of image recognition, natural language processing(NLP), bioinformatics, computer vision domains and many other fields. DNN applications require huge models as they are computationally expensive, over-parameterized and have high memory footprints which becomes a bottleneck in deployment on embedded devices. Optimization of DNN models is crucial. In this paper, we have summarized the recent works done on optimization of DNNs using various pruning techniques and their comparisons. Pruning technique aims at eliminating less salient connections, neurons, channels, filters, thereby making DNNs model easier to deploy on embedded devices.

Kernel ridge regression (KRR) is a powerful method for nonparametric regression. The time and space complexity of computing the KRR estimate directly are O(n3) and O(n2) , respectively, which are prohibitive for large-scale data sets, where n is the number of data. In this article, we propose a novel random sketch technique based on the circulant matrix that achieves savings in storage space and accelerates the solution of the KRR approximation. The circulant matrix has the following advantages: It can save time complexity by using the fast Fourier transform (FFT) to compute the product of matrix and vector, its space complexity is linear, and the circulant matrix, whose entries in the first column are independent of each other and obey the Gaussian distribution, is almost as effective as the i.i.d. Gaussian random matrix for approximating KRR. Combining the characteristics of the circulant matrix and our careful design, theoretical analysis and experimental results demonstrate that our proposed sketch method, making the estimate kernel methods scalable and practical for large-scale data problems, outperforms the state-of-the-art KRR estimates in time complexity while retaining similar accuracies. Meanwhile, our sketch method provides the theoretical bound that keeps the optimal convergence rate for approximating KRR.

In the future, vehicles will be equipped with increasingly advanced interactive intelligent electronic devices, which will induce drivers to conduct secondary tasks, thereby leading to distractions. Therefore, the detection and early warning of driver distraction are essential for improving driving safety and pose an important challenge in intelligent transportation systems. Previous studies used traditional machine learning and deep learning transfer models, which have the disadvantages of complicated and time-consuming manual feature engineering, strong subjectivity, and weak generalization performance. In this paper, we propose a fine-grained detection method for driver distraction based on neural architecture search. First, we design an automatic construction algorithm for deep convolutional neural networks based on neural architecture search, which automatically searches for the optimal deep convolutional neural network architecture without human involvement. In addition, we fuse driver-related multisource perception information, use an automatically constructed deep convolutional neural network to extract high-dimensional mapping features, and implement fine-grained detection of various types of driver distraction states. The results on a large-scale multimodal driver distraction dataset demonstrate that our method can efficiently search an optimal deep convolutional neural network, which can quickly converge, and can accurately detect the considered types of driver distraction states, the average detection accuracy reaches 99.7796%; moreover, it has satisfactory robustness.

We consider the wavelet-based estimators of mean regression function with long memory moving average errors and investigate their asymptotic rates of convergence based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large range of Besov function classes \(B^{s}_{p,q}\). Therefore, in the presence of long memory non-Gaussian moving average noise, wavelet estimators still achieve nearly optimal convergence rates and provide explicitly the extraordinary local adaptability. The theory is illustrated with some numerical examples.

In theory, recent results in nonparametric regression show that neural network estimates are able to achieve good rates of convergence provided suitable assumptions on the structure of the regression function are imposed. However, these theoretical analyses cannot explain the practical success of neural networks since the theoretically studied estimates are defined by minimizing the empirical L_2 risk over a class of neural networks and in practice, solving this kind of minimization problem is not feasible. Consequently, the neural networks examined in theory cannot be implemented as they are defined. This means that neural network in applications differ from the ones that are analyzed theoretically. In this thesis we narrow the gap between theory and practice. We deal with neural network regression estimates for (p,C)-smooth regression functions m that satisfy a projection pursuit model. We construct three implementable neural network estimates and show that each of them achieve up to a logarithmic factor the optimal univariate rate of convergence. Firstly, for univariate regression functions with p contained in [-1/2,1] we construct a neural network estimate with one hidden layer where the weights are learned via gradient descent. The starting weights are randomly chosen from an interval independently of the data. The interval is large enough to guarantee that the estimate is close to a piecewise constant approximation. Secondly, for multivariate regression functions with p contained in (0,1] we construct a neural network estimate with one hidden layer where the weights are learned via gradient descent. The initial weights are chosen from specific intervals dependently on the data and the projection directions. This choice guarantees that the estimate is close to a piecewise constant approximation. The projection directions are repeatedly chosen randomly. Lastly, for multivariate regression functions with p>0 we construct a multilayer neural network estimate. The value of the inner weights are prescribed dependently on the projection directions by a new approximation result for a projection pursuit model by piecewise polynomials. The outer weights are chosen by solving a linear equation system. The projection directions are repeatedly chosen randomly. Since we are able to show a rate of convergence that is independent of the dimension of the data our second and third estimates are able to circumvent the curse of dimensionality.