Hyperparameters play a critical role in the performances of many machine learning methods. Determining their best settings or Hyperparameter Optimization (HPO) faces difficulties presented by the large number of hyperparameters as well as the excessive training time. In this paper, we develop an effective approach to reducing the total amount of required training time for HPO. In the initialization, the nested Latin hypercube design is used to select hyperparameter configurations for two types of training, which are, respectively, heavy training and light training. We propose a truncated additive Gaussian process model to calibrate approximate performance measurements generated by light training, using accurate performance measurements generated by heavy training. Based on the model, a sequential model-based algorithm is developed to generate the performance profile of the configuration space as well as find optimal ones. Our proposed approach demonstrates competitive performance when applied to optimize synthetic examples, support vector machines, fully connected networks and convolutional neural networks.

In this chapter we review the main literature related to the recent advancement of deep neural-kernel architecture, an approach that seek the synergy between two powerful class of models, i.e. kernel-based models and artificial neural networks. The introduced deep neural-kernel framework is composed of a hybridization of the neural networks architecture and a kernel machine. More precisely, for the kernel counterpart the model is based on Least Squares Support Vector Machines with explicit feature mapping. Here we discuss the use of one form of an explicit feature map obtained by random Fourier features. Thanks to this explicit feature map, in one hand bridging the two architectures has become more straightforward and on the other hand one can find the solution of the associated optimization problem in the primal, therefore making the model scalable to large scale datasets. We begin by introducing a neural-kernel architecture that serves as the core module for deeper models equipped with different pooling layers. In particular, we review three neural-kernel machines with average, maxout and convolutional pooling layers. In average pooling layer the outputs of the previous representation layers are averaged. The maxout layer triggers competition among different input representations and allows the formation of multiple sub-networks within the same model. The convolutional pooling layer reduces the dimensionality of the multi-scale output representations. Comparison with neural-kernel model, kernel based models and the classical neural networks architecture have been made and the numerical experiments illustrate the effectiveness of the introduced models on several benchmark datasets.

It seems that all of the work in machine learning -- starting from early research in the 1950s -- cumulated with the creation of the neural network. Successively, algorithm after new algorithm were proposed, from logistic regression to support vector machines, but the neural network is, very literally, the algorithm of algorithms and the pinnacle of machine learning. It's a universal generalization of what machine learning is, instead of one attempt of doing it. In this sense, it is more of a framework and a concept than simply an algorithm, and this is evident given the massive amount of freedom in constructing neural networks -- hidden layer & node counts, activation functions, optimizers, loss functions, network types (convolutional, recurrent, etc.), and specialized layers (batch norm, dropout, etc.), to name a few. From this perspective of neural networks being a concept rather than a rigid algorithm comes a very interesting corollary: any machine learning algorithm, be it decision trees or k-nearest neighbors, can be represented using a neural network.

This paper presents the impact of using quantization on the efficiency of multi-class text classification in the training process of a support vector machine (SVM). This work is focused on comparing the efficiency of SVM model trained using reduced precision with its original form. The main advantage of using quantization is decrease in computation time and in memory footprint on the dedicated hardware platform which supports low precision computation like GPU (16-bit) or FPGA (any bit-width). The paper presents the impact of a precision reduction of the SVM training process on text classification accuracy. The implementation of the CPU was performed using the OpenMP library. Additionally, the results of the implementation of the GPU using double, single and half precision are presented.

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Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to $\infty$ with fixed ratio $\alpha=n/p$. This family covers a broad range of commonly used classifiers including support vector machine, distance weighted discrimination, and penalized logistic regression. Our result can be used to establish the phase transition boundary for the separability of two classes. We assume that the data are generated from a single multivariate Gaussian distribution with arbitrary covariance structure. We explore two special choices for the covariance matrix: spiked population model and two layer neural networks with random first layer weights. The method we used for deriving the closed-form expression is from statistical physics known as the replica method. Our asymptotic results match simulations already when $n,p$ are of the order of a few hundreds. For two layer neural networks, we reproduce the recently developed `double descent' phenomenology for several classification models. We also discuss some statistical insights that can be drawn from these analysis.

Since the inception of SVMs [1], the interest for this kind of supervised learning method has only grown over the years [2], so that it has become a well established tool both for classification and regression [3]. SVMs are regarded as the most prominent exemplar of kernel methods, which solve complex machine learning problems by using linear estimation methods on a high dimensional feature space [4]. They are intensely employed in a myriad of applications, including object segmentation [5], video surveillance [6], drug discovery [7], and cancer genomics [8]. The SVM framework models a classification problem as a maximum margin optimization problem, where the decision boundary that has the largest distance (margin) to separate the training points of different classes is searched. There is a primal form of the optimization problem, where the weights to be optimized are associated with the input features, i.e., there is one weight per each input feature. There is also a dual form, where the weights are associated with the training samples, i.e., one weight per each training sample. In the dual form, the weights are Lagrange multipliers of a suitable Lagrangian function. The fewer variables to be optimized, the easier the optimization problem, so dual formulations are preferred for classification tasks with many input features [9]. This work has been submitted to the IEEE for possible publication.

Over the past few years, there has been a considerable spread of microarray technology in many biological patterns, particularly in those pertaining to cancer diseases like leukemia, prostate, colon cancer, etc. The primary bottleneck that one experiences in the proper understanding of such datasets lies in their dimensionality, and thus for an efficient and effective means of studying the same, a reduction in their dimension to a large extent is deemed necessary. This study is a bid to suggesting different algorithms and approaches for the reduction of dimensionality of such microarray datasets. This study exploits the matrix-like structure of such microarray data and uses a popular technique called Non-Negative Matrix Factorization (NMF) to reduce the dimensionality, primarily in the field of biological data. Classification accuracies are then compared for these algorithms. This technique gives an accuracy of 98%.

Support vector machines (SVM) is a supervised machine learning technique. And, even though it's mostly used in classification, it can also be applied to regression problems. SVMs define a decision boundary along with a maximal margin that separates almost all the points into two classes. Support vector machines are an improvement over maximal margin algorithms. Its biggest advantage is that it can define both a linear or a non-linear decision boundary by using kernel functions.

The task of supervised machine learning is given a set of recorded observations and their outcomes to predict the outcome of new observations. Standard classification techniques aim for the highest overall accuracy or, equivalently, for the smallest total error, and include among others support vector machines, Bayesian classifiers, logistic regression, decision tree classifiers such as CART [6] and C4.5 [38], and ensemble methods which build several classifiers and aggregate their predictions such as Bagging [4], AdaBoost [16] and Random Forests [5]. Of particular interest in certain domains are binary classifiers which deal with cases where only two classes of outcomes are considered, such as fraudulent and legitimate credit card transactions, responders and non-responders to a marketing campaign, patients with and without cancer, intrusive and authorised network access, and defaulting and repaying debtors to name a few. In most of these cases, one of the classes is a small minority and consequently traditional classifiers might classify all of its members as belonging to the majority class without any significant overall accuracy loss. The severity of this class imbalance becomes more noticeable when failing to correctly predict a minority class member is more costly than doing so with a member of the majority class, as the case often is. A remedy to the undesirable situation just described are classifiers which, instead of accuracy, take misclassification costs into account and are thus termed cost-sensitive. We illustrate this idea in the credit card fraud detection framework: accepting a fraudulent transaction as legitimate incurs a cost equal to its amount.