The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated concerning a subset of points called reference points. Its simple formulation has attracted several recent works on extensions and applications. In this paper, we aim to address some open questions related to the MLM. First, we detail theoretical aspects that assure the interpolation and universal approximation capabilities of the MLM, which were previously only empirically verified. Second, we identify the task of selecting reference points as having major importance for the MLM's generalization capability; furthermore, we assess several clustering-based methods in regression scenarios. Based on an extensive empirical evaluation, we conclude that the evaluated methods are both scalable and useful. Specifically, for a small number of reference points, the clustering-based methods outperformed the standard random selection of the original MLM formulation.

The traditional paradigm for developing machine prognostics usually relies on generalization from data acquired in experiments under controlled conditions prior to deployment of the equipment. Detecting or predicting failures and estimating machine health in this way assumes that future field data will have a very similar distribution to the experiment data. However, many complex machines operate under dynamic environmental conditions and are used in many different ways. This makes collecting comprehensive data very challenging, and the assumption that pre-deployment data and post-deployment data follow very similar distributions is unlikely to hold. Transfer Learning (TL) refers to methods for transferring knowledge learned in one setting (the source domain) to another setting (the target domain). In this work, we present a TL method for predicting Remaining Useful Life (RUL) of equipment, under the assumption that labels are available only for the source domain and not the target domain. This setting corresponds to generalizing from a limited number of run-to-failure experiments performed prior to deployment into making prognostics with data coming from deployed equipment that is being used under multiple new operating conditions and experiencing previously unseen faults. We employ a deviation detection method, Consensus Self-Organizing Models (COSMO), to create transferable features for building the RUL regression model. These features capture how different target equipment is in comparison to its peers. The efficiency of the proposed TL method is demonstrated using the NASA Turbofan Engine Degradation Simulation Data Set. Models using the COSMO transferable features show better performance than other methods on predicting RUL when the target domain is more complex than the source domain.

This first video in the logistic regression series introduces this powerful classification algorithm. The logistic regression algorithm is used when the dependent variable or target variable is categorical. Simple Logistic Regression and Multinomial Logistic Regression are explained. This second video in the logistic regression series compares logistic regression with linear regression in terms of their purpose, use cases, equations, error minimizations, and assumptions. This third video in the logistic regression series covers the four ways of preprocessing data before performing logistic regression: missing data handling, categorical data handling, splitting into train and test set, and feature scaling.

In this paper, we study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noiseless case, we provide matching upper and lower bounds on sample complexity for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, we develop upper and matching minimax lower bounds for estimation error. We also consider the debiased sparse group Lasso and investigate its asymptotic property for the purpose of statistical inference. Finally, numerical studies are provided to support the theoretical results.

The Internet of Things (IoT) will be a main data generation infrastructure for achieving better system intelligence. However, the extensive data collection and processing in IoT also engender various privacy concerns. This paper provides a taxonomy of the existing privacy-preserving machine learning approaches developed in the context of cloud computing and discusses the challenges of applying them in the context of IoT. Moreover, we present a privacy-preserving inference approach that runs a lightweight neural network at IoT objects to obfuscate the data before transmission and a deep neural network in the cloud to classify the obfuscated data. Evaluation based on the MNIST dataset shows satisfactory performance.

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different cases, namely: each function $f_i$ is strongly convex and smooth, each function is either strongly convex or smooth, and when it is convex but neither strongly convex nor smooth. Our approach is based on the dual of an appropriately formulated primal problem, which includes a graph that models the communication restrictions. We propose distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional optimal cost related to the spectral properties of the network. Initially, we focus on functions for which we can explicitly minimize its Legendre-Fenchel conjugate, i.e., admissible or dual friendly functions. Then, we study distributed optimization algorithms for non-dual friendly functions, as well as a method to improve the dependency on the parameters of the functions involved. Numerical analysis of the proposed algorithms is also provided.

This paper extends the idea of Universum learning [1, 2] to single-class learning problems. We propose Single Class Universum-SVM setting that incorporates a priori knowledge (in the form of additional data samples) into the single class estimation problem. These additional data samples or Universum belong to the same application domain as (positive) data samples from a single class (of interest), but they follow a different distribution. Proposed methodology for single class U-SVM is based on the known connection between binary classification and single class learning formulations [3]. Several empirical comparisons are presented to illustrate the utility of the proposed approach.

Reproducible research in Machine Learning has seen a salutary abundance of progress lately: workflows, transparency, and statistical analysis of validation and test performance. We build on these efforts and take them further. We offer a principled experimental design methodology, based on linear mixed models, to study and separate the effects of multiple factors of variation in machine learning experiments. This approach allows to account for the effects of architecture, optimizer, hyper-parameters, intentional randomization, as well as unintended lack of determinism across reruns. We illustrate that methodology by analyzing Matching Networks, Prototypical Networks and TADAM on the miniImagenet dataset.

In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep clustering framework and compared with the possible classical implementation. Our investigation shows that the proposed quantum version of deep clustering formulation demonstrates a significant performance gain (exponential speed up gains in many sections) against the possible classical implementation. The proposed theoretical quantum deep clustering framework is also interesting & novel research towards the quantum-classical machine learning formulation to articulate the maximum performance.

Despite the development of numerous adaptive optimizers, tuning the learning rate of stochastic gradient methods remains a major roadblock to obtaining good practical performance in machine learning. Rather than changing the learning rate at each iteration, we propose an approach that automates the most common hand-tuning heuristic: use a constant learning rate until "progress stops," then drop. We design an explicit statistical test that determines when the dynamics of stochastic gradient descent reach a stationary distribution. This test can be performed easily during training, and when it fires, we decrease the learning rate by a constant multiplicative factor. Our experiments on several deep learning tasks demonstrate that this statistical adaptive stochastic approximation (SASA) method can automatically find good learning rate schedules and match the performance of hand-tuned methods using default settings of its parameters. The statistical testing helps to control the variance of this procedure and improves its robustness.