Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending randomized CD to nonsmooth nonconvex settings, we develop a coordinate subgradient method that randomly updates block-coordinate variables by using block composite subgradient mapping. This method converges asymptotically to critical points with proven sublinear convergence rate for certain optimality measures. Second, we develop a randomly permuted CD method with two alternating steps: linearizing the concave part and cycling through variables. We prove asymptotic convergence to critical points and sublinear complexity rate for objectives with both smooth and concave parts. Third, we extend accelerated coordinate descent (ACD) to nonsmooth and nonconvex optimization to develop a novel randomized proximal DC algorithm whereby we solve the subproblem inexactly by ACD. Convergence is guaranteed with at most a few number of ACD iterations for each DC subproblem, and convergence complexity is established for identification of some approximate critical points. Fourth, we further develop the third method to minimize certain ill-conditioned nonconvex functions: weakly convex functions with high Lipschitz constant to negative curvature ratios. We show that, under specific criteria, the ACD-based randomized method has superior complexity compared to conventional gradient methods. Finally, an empirical study on sparsity-inducing learning models demonstrates that CD methods are superior to gradient-based methods for certain large-scale problems.

This is because ML is effective to handle and interpret big data sets for the purpose of finding certain patterns from the data. In particular, Deep Neural Network (DNN), which is based on an Artificial Neural Network (ANN) with multiple hidden layers between input and output layers allows to handle complex shapes with nonlinear functions with multidimensional input data. DNN has been successfully used in a large number of practical applications. Well trained neural network then provides precise pattern recognition based on data sets in real time. These features, big data recognition and real time estimation of nonlinear functions, of ML approaches are attractive to dynamics and control engineers who are handling nonlinear system dynamics with real world data. There have been several previous studies on applying ML, DNN, or other big-data handling techniques to rigid multibody system problems.

Deep networks are well-known to be fragile to adversarial attacks. Using several standard image datasets and established attack mechanisms, we conduct an empirical analysis of deep representations under attack, and find that the attack causes the internal representation to shift closer to the "false" class. Motivated by this observation, we propose to regularize the representation space under attack with metric learning in order to produce more robust classifiers. By carefully sampling examples for metric learning, our learned representation not only increases robustness, but also can detect previously unseen adversarial samples. Quantitative experiments show improvement of robustness accuracy by up to 4\% and detection efficiency by up to 6\% according to Area Under Curve (AUC) score over baselines.

Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and the outputs of unstructured predictors simultaneously. As most structural models, the GCRF model does not scale well with large networks. One of the approaches consists of performing calculations on factor graphs (if it is possible) rather than on the full graph, which is more computationally efficient. The Kronecker product of the graphs appears to be a natural choice for a graph decomposition. However, this idea is not straightforwardly applicable for GCRF, since characterizing a Laplacian spectrum of the Kronecker product of graphs, which GCRF is based on, from spectra of its factor graphs has remained an open problem. In this paper we apply new estimations for the Laplacian eigenvalues and eigenvectors, and achieve high prediction accuracy of the proposed models, while the computational complexity of the models, compared to the original GCRF model, is improved from $O(n_{1}^{3}n_{2}^{3})$ to $O(n_{1}^{3} + n_{2}^{3})$. Furthermore, we study the GCRF model with a non-Kronecker graph, where the model consists of finding the nearest Kronecker product of graph for an initial graph. Although the proposed models are more complex, they achieve high prediction accuracy too, while the execution time is still much better compare to the original GCRF model. The effectiveness of the proposed models is characterized on three types of random networks where the proposed models were consistently away more accurate than the previously presented GCRF model for multiscale networks [Jesse Glass and Zoran Obradovic. Structured regression on multiscale networks. IEEE Intelligent Systems, 32(2):23-30, 2017.].

We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal $O(1/T)$ convergence rate in expectation. We consider a simple, non-uniform averaging strategy of Lacoste-Julien et al. (2011) and prove that it achieves the optimal $O(1/T)$ convergence rate with high probability. Our proof uses a recently developed generalization of Freedman's inequality. Finally, we compare several of these algorithms experimentally and show that this non-uniform averaging strategy outperforms many standard techniques, and with smaller variance.

Real estate appraisal is a complex and important task, that can be made more precise and faster with the help of automated valuation tools. Usually the value of some property is determined by taking into account both structural and geographical characteristics. However, while geographical information is easily found, obtaining significant structural information requires the intervention of a real estate expert, a professional appraiser. In this paper we propose a Web data acquisition methodology, and a Machine Learning model, that can be used to automatically evaluate real estate properties. This method uses data from previous appraisal documents, from the advertised prices of similar properties found via Web crawling, and from open data describing the characteristics of a corresponding geographical area. We describe a case study, applicable to the whole Italian territory, and initially trained on a data set of individual homes located in the city of Turin, and analyze prediction and practical applicability.

In this paper, we address the challenging problem of learning from imbalanced data using a Nearest-Neighbor (NN) algorithm. In this setting, the minority examples typically belong to the class of interest requiring the optimization of specific criteria, like the F-Measure. Based on simple geometrical ideas, we introduce an algorithm that reweights the distance between a query sample and any positive training example. This leads to a modification of the Voronoi regions and thus of the decision boundaries of the NN algorithm. We provide a theoretical justification about the weighting scheme needed to reduce the False Negative rate while controlling the number of False Positives. We perform an extensive experimental study on many public imbalanced datasets, but also on large scale non public data from the French Ministry of Economy and Finance on a tax fraud detection task, showing that our method is very effective and, interestingly, yields the best performance when combined with state of the art sampling methods.

Power load forecast with Machine Learning is a fairly mature application of artificial intelligence and it is indispensable in operation, control and planning. Data selection techniqies have been hardly used in this application. However, the use of such techniques could be beneficial provided the assumption that the data is identically distributed is clearly not true in load forecasting, but it is cyclostationary. In this work we present a fully automatic methodology to determine what are the most adequate data to train a predictor which is based on a full Bayesian probabilistic model. We assess the performance of the method with experiments based on real publicly available data recorded from several years in the United States of America.

Data Science, Business Analytics or Business Intelligence all of these are birds of the same nest and they have some features in common, It is safe to say that they are same same but different. One of the common features is the algorithms and models to compare, analyse and predict stuff. Some of the most commonly used machine learning algorithms with mathematics are explained as follows. Linear regression tries to represent the relationship between two variables by fitting a linear equation. Where, One variable is illustrative, and the other is supposed to be dependent.

Suppose we have users, for each user, we have: user_id, user_name, user_job title, user_skills, user_workExperience. I need to cluster the user based on their skill and work experience( long text data), put the users into groups. I was searching about how to clustering text data but still didn't find a good example to follow" step by step". Based on the data I have I think I should use unsupervised approach (as the data I have is not labeled), I found that I can use K-Mean or hierarchical clustering, but I'm stuck in how to find: K "number of clustering with K-Mean". Also, I don't know what is the best way to prepare the long text before fit into the clustering algorithm.