In real-world applications, we can encounter situations when a well-trained model has to be used to predict from a damaged dataset. The damage caused by missing or corrupted values can be either on the level of individual instances or on the level of entire features. Both situations have a negative impact on the usability of the model on such a dataset. This paper focuses on the scenario where entire features are missing which can be understood as a specific case of transfer learning. Our aim is to experimentally research the influence of various imputation methods on the performance of several classification models. The imputation impact is researched on a combination of traditional methods such as k-NN, linear regression, and MICE compared to modern imputation methods such as multi-layer perceptron (MLP) and gradient boosted trees (XGBT). For linear regression, MLP, and XGBT we also propose two approaches to using them for multiple features imputation. The experiments were performed on both real world and artificial datasets with continuous features where different numbers of features, varying from one feature to 50%, were missing. The results show that MICE and linear regression are generally good imputers regardless of the conditions. On the other hand, the performance of MLP and XGBT is strongly dataset dependent. Their performance is the best in some cases, but more often they perform worse than MICE or linear regression.

Standard algorithms in detection systems perform insufficiently when dealing with malware passed through obfuscation tools. We illustrate this studying in detail an open source metamorphic software, making use of a hybrid framework to obtain the relevant features from binaries. We then provide an improved alternative solution based on adversarial risk analysis which we illustrate describe with an example. KEYWORDS: Adversarial Risk Analysis, Malware Obfuscation, Cybersecurity 1 INTRODUCTION The digital era is bringing along new global threats among which cybersecurity related ones emerge as truly worrisome, see for example the evolution of the Global Risks Map from the World Economic Forum (2017, 2018, 2019). Indeed, the operation of critical cyber infrastructures relies on components which could be cyber attacked, both incidentally and intentionally, suffering major performance degradation, Rao et al. (2016).

We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities is narrowed to just two. Next we consider explicability in development, which means ability to make incremental improvement in prediction accuracy based on observed deficiency of the system. Inherent stochasticity of neural network based classifiers can be interpreted using likelihood randomness explicability. Finally, sureness explicability indicates confidence of the classifying system to make any prediction at all. These concepts are examined in the framework of pairwise coupling, which is a non-trainable metamodel that originated during development of support vector machines. Several methodologies are evaluated, of which the key one is shown to be the choice of the pairwise coupling method. We compare two methods: the established Wu-Lin-Weng method with the recently proposed Bayes covariant method. Our experiments indicate that the Wu-Lin-Weng method gives more weight to a single pairwise classifier, whereas the latter tries to balance information from the whole matrix of pairwise likelihoods. This translates into higher accuracy, and better sureness predictions for the Bayes covariant method. Pairwise coupling methodology has its costs, especially in terms of the number of parameters (but not necessarily in terms of training costs). However, when additional explicability aspects beyond accuracy are desired in an application, the pairwise coupling models are a promising alternative to the established methodology.

Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of a dependent data stream remains largely unexplored. In this paper, we show that the well-known OMF algorithm for i.i.d. Furthermore, we extend the convergence result to the case when we can only approximately solve each step of the optimization problems in the algorithm. For applications, we demonstrate dictionary learning from a sequence of images generated by a Markov Chain Monte Carlo (MCMC) sampler. Lastly, by combining online nonnegative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning, which extracts'network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique on real-world text data. I NTRODUCTION In modern data analysis, a central step is to find a low-dimensional representation to better understand, compress, or convey the key phenomena captured in the data. Matrix factorization provides a powerful setting for one to describe data in terms of a linear combination of factors or atoms. In this setting, we have a data matrix X R d n, and we seek a factorization of X into the product W H for W R d r and H R r n . This problem has gone by many names over the decades, each with different constraints: dictionary learning, factor analysis, topic modeling, component analysis. It has applications in text analysis, image reconstruction, medical imaging, bioinformatics, and many other scientific fields more generally [SGH02, BB05, BBL 07, CWS 11, TN12, BMB 15, RPZ 18]. Each column of the data matrix is approximated by a linear combination of the columns of the dictionary matrix. Online matrix factorization is a problem setting where data are accessed in a streaming manner and the matrix factors should be updated each time. That is, we get draws of X from some distribution π and seek the best factorization such that the expected loss E X πnull null X W H null 2 F null is small. This is a relevant setting in today' s data world, where large companies, scientific instruments, and healthcare systems are collecting massive amounts of data every day . One cannot compute with the entire 1 arXiv:1911.01931v3 There are several algorithms for computing factorizations of various kinds in an online context. Many of them have algorithmic convergence guarantees, however, all these guarantees require that data are sampled at each iteration i.i.d. with respect to previous iterations. In all of the application examples mentioned above, one may make an argument for (nearly) identical distributions, but never for independence.

This article aims to share with you some methods to implement linear regression on a real dataset, which includes data including, data analysis, datasets split and regression construction itself. To learn PyTorchwell, I'd demonstrate regression by PyTorchand show you the charm of PyTorchin forward and backward. This story has a hypothesis that all the readers have been familiar with the principle of linear regression. Readers should understand the meaning and solution methods of W and b of the equation Y XW b. To have a better experience, it's better to understand the gradient descent method that can be used to solve the problem and understand the MSE used to evaluate the regression performance.

For example, suppose you want to build a simple linear regression model using an m-dimensional training data set. If the model uses the gradient descent algorithm to minimize the objective function in order to determine the weights w_0, w_1, w_2, …,w_m, then we can have an optimizer such as GradientDescent(eta, n_iter). Here eta (learning rate) and n_iter (number of iterations) are the hyperparameters that would have to be adjusted in order to obtain the best values for the model parameters w_0, w_1, w_2, …,w_m. For more information about this, see the following example: Machine Learning: Python Linear Regression Estimator Using Gradient Descent. Here, n_iter is the number of iterations, eta0 is the learning rate, and random_state is the seed of the pseudo random number generator to use when shuffling the data.

We live in a world in which machine learning is at the core of the fourth industrial revolution. Linear regression is one of the simplest and most widely used machine learning techniques. There are a plethora of practical applications of linear regression. For example, obesity can be used to predict the chances of developing type 2 diabetes. Or, a student's GPA can be predicted based on the number of hours he/she spends studying.

In the previous article, we studied Logistic Regression. One thing that I believe is that if we can correlate anything with us or our lives, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans.

Combining data from varied sources has considerable potential for knowledge discovery: collaborating data parties can mine data in an expanded feature space, allowing them to explore a larger range of scientific questions. However, data sharing among different parties is highly restricted by legal conditions, ethical concerns, and / or data volume. Fueled by these concerns, the fields of cryptography and distributed learning have made great progress towards privacy-preserving and distributed data mining. However, practical implementations have been hampered by the limited scope or computational complexity of these methods. In this paper, we greatly extend the range of analyses available for vertically partitioned data, i.e., data collected by separate parties with different features on the same subjects. To this end, we present a novel approach for privacy-preserving generalized linear models, a fundamental and powerful framework underlying many prediction and classification procedures. We base our method on a distributed block coordinate descent algorithm to obtain parameter estimates, and we develop an extension to compute accurate standard errors without additional communication cost. We critically evaluate the information transfer for semi-honest collaborators and show that our protocol is secure against data reconstruction. Through both simulated and real-world examples we illustrate the functionality of our proposed algorithm. Without leaking information, our method performs as well on vertically partitioned data as existing methods on combined data -- all within mere minutes of computation time. We conclude that our method is a viable approach for vertically partitioned data analysis with a wide range of real-world applications.

The Pearson's $\chi^2$ test and residual deviance test are two classical goodness-of-fit tests for binary regression models such as logistic regression. These two tests cannot be applied when we have one or more continuous covariates in the data, a quite common situation in practice. In that case, the most widely used approach is the Hosmer-Lemeshow test, which partitions the covariate space into groups according to quantiles of the fitted probabilities from all the observations. However, its grouping scheme is not flexible enough to explore how to adversarially partition the data space in order to enhance the power. In this work, we propose a new methodology, named binary regression adaptive grouping goodness-of-fit test (BAGofT), to address the above concern. It is a two-stage solution where the first stage adaptively selects candidate partitions using "training" data, and the second stage performs $\chi^2$ tests with necessary corrections based on "test" data. A proper data splitting ensures that the test has desirable size and power properties. From our experimental results, BAGofT performs much better than Hosmer-Lemeshow test in many situations.