We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for compressive sensing inversion based on convolutional factor analysis is developed. The proposed algorithm provides reconstructed images as well as features, which can be directly used for recognition ($e.g.$, classification) tasks. When a deep (multilayer) model is constructed, a stochastic unpooling process is employed to build a generative model. During reconstruction and testing, we project the upper layer dictionary to the data level and only a single layer deconvolution is required. We demonstrate that using $\sim30\%$ (relative to pixel numbers) compressed measurements, the proposed model achieves the classification accuracy comparable to the original data on MNIST. We also observe that when the compressed measurements are very limited ($e.g.$, $<10\%$), the upper layer dictionary can provide better reconstruction results than the bottom layer.

This paper studies the problem of multivariate linear regression where a portion of the observations is grossly corrupted or is missing, and the magnitudes and locations of such occurrences are unknown in priori. To deal with this problem, we propose a new approach by explicitly consider the error source as well as its sparseness nature. An interesting property of our approach lies in its ability of allowing individual regression output elements or tasks to possess their unique noise levels. Moreover, despite working with a non-smooth optimization problem, our approach still guarantees to converge to its optimal solution. Experiments on synthetic data demonstrate the competitiveness of our approach compared with existing multivariate regression models. In addition, empirically our approach has been validated with very promising results on two exemplar real-world applications: The first concerns the prediction of \textit{Big-Five} personality based on user behaviors at social network sites (SNSs), while the second is 3D human hand pose estimation from depth images. The implementation of our approach and comparison methods as well as the involved datasets are made publicly available in support of the open-source and reproducible research initiatives.

In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent random matrix advances, when both the dimension of data $p$ and their number $n$ grow large at the same rate, we show that the LS-SVM decision function converges to a normal-distributed variable, the mean and variance of which depend explicitly on a local behavior of the kernel function. This theoretical result is then applied to the MNIST data sets which, despite their non-Gaussianity, exhibit a surprisingly similar behavior. Our analysis provides a deeper understanding of the mechanism into play in SVM-type methods and in particular of the impact on the choice of the kernel function as well as some of their theoretical limits.

Spectral dimensionality reduction is frequently used to identify low-dimensional structure in high-dimensional data. However, learning manifolds, especially from the streaming data, is computationally and memory expensive. In this paper, we argue that a stable manifold can be learned using only a fraction of the stream, and the remaining stream can be mapped to the manifold in a significantly less costly manner. Identifying the transition point at which the manifold is stable is the key step. We present error metrics that allow us to identify the transition point for a given stream by quantitatively assessing the quality of a manifold learned using Isomap. We further propose an efficient mapping algorithm, called S-Isomap, that can be used to map new samples onto the stable manifold. We describe experiments on a variety of data sets that show that the proposed approach is computationally efficient without sacrificing accuracy.

This is the second installment in a three-part series covering AI2 and machine learning. Be sure to read Part 1 for an introduction to AI2. AI2 is an "analyst-in-the-loop" system, meaning that it exploits the expertise of a security analyst to improve itself. A "human-in-the-loop" system is used to generate more supervised examples for the machine learning stage to use in an iterative training algorithm. This is exactly what AI2 does, allowing feedback to make the machine gradually smarter in the security domain.

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential, integro-differential, and fractional order operators. Here, Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations. Such observations may come from experiments or "black-box" computer simulations.

Looking at this text, we already see complexity emerging. As a human reader, I'm sure you'll say this is a negative review, and undoubtedly there are some clearly negative words ("dreadful", "confusing", "terrible"). But to a high degree, negativity comes from negated positive words: "lacking achievement", "wasn't very funny", "not as good as she could have given". So clearly we cannot just look at single words in isolation, but at sequences of words – n-grams (bigrams, trigrams, …) as they say in natural language processing. The question is though, at how many consecutive words should we look?

Think Stats: Exploratory Data Analysis in Python Think Stats: Exploratory Data Analysis in Python by Allen B. Downey, 2014

P-values for coefficients of cylinders, horsepower and acceleration are all greater than 0.05. This means that the relationship between the dependent and these independent variables is not significant at the 95% certainty level. I'll drop 2 of these variables and try again. High p-values for these independent variables do not mean that they definitely should not be used in the model. It could be that some other variables are correlated with these variables and making these variables less useful for prediction (check Multicollinearity).

Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statistical problem to identify the Gaussian graphical model from a sample of a given size. Different approaches for Gaussian graphical model selection are suggested in the literature. One of them is based on considering the family of individual conditional independence tests. The application of this approach leads to the construction of a variety of multiple testing statistical procedures for Gaussian graphical model selection. An important characteristic of these procedures is its error rate for a given sample size. In existing literature great attention is paid to the control of error rates for incorrect edge inclusion (Type I error). However, in graphical model selection it is also important to take into account error rates for incorrect edge exclusion (Type II error). To deal with this issue we consider the graphical model selection problem in the framework of the multiple decision theory. The quality of statistical procedures is measured by a risk function with additive losses. Additive losses allow both types of errors to be taken into account. We construct the tests of a Neyman structure for individual hypotheses and combine them to obtain a multiple decision statistical procedure. We show that the obtained procedure is optimal in the sense that it minimizes the linear combination of expected numbers of Type I and Type II errors in the class of unbiased multiple decision procedures.