We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of $Af$) and the inverse (estimation of $f$) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations $n$ grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in $n$ but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set.

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit matrix completion problem. Our approach relies on tools from machine learning theory: empirical risk minimization and its convex relaxations. We propose an algorithm to compute a variational approximation of the pseudo-posterior. Thanks to the convex relaxation, the corresponding minimization problem is bi-convex, and thus the method behaves well in practice. We also study the performance of this variational approximation through PAC-Bayesian learning bounds. On the contrary to previous works that focused on upper bounds on the estimation error of M with various matrix norms, we are able to derive from this analysis a PAC bound on the prediction error of our algorithm. We focus essentially on convex relaxation through the hinge loss, for which we present the complete analysis, a complete simulation study and a test on the MovieLens data set. However, we also discuss a variational approximation to deal with the logistic loss.

Researchers have used from 30 days to several years of daily returns as source data for clustering financial time series based on their correlations. This paper sets up a statistical framework to study the validity of such practices. We first show that clustering correlated random variables from their observed values is statistically consistent. Then, we also give a first empirical answer to the much debated question: How long should the time series be? If too short, the clusters found can be spurious; if too long, dynamics can be smoothed out.

Machine Learning, which is a process to predict future patterns and incidents based on the models created out of past data, is definitely the most important part of the success of the Internet of Things in the enterprise and consumer space. The main reason is that without machine learning the entire backbone of the Internet of Things - event acquisition, event processing, event storage and event reporting - is merely a live display of events happening elsewhere and will not provide any value to its consumers. Think of a smart monitor in an oil well that monitors various climatic conditions and other factors that can cause a failure; unless the monitor is able to predict of a failure and corrects itself the usage of such solution is quite limited. MLPaaS - Azure Vs AWS In that context, Machine Learning Platform as a Service (MLPaaS) has been a major component of the major cloud platforms. Both Azure and AWS have equivalent services, the below thoughts are comparison of major building blocks of a machine learning service and how the respective cloud providers handle them.

In order to push the performance on realistic computer vision tasks, the number of classes in modern benchmark datasets has significantly increased in recent years. This increase in the number of classes comes along with increased ambiguity between the class labels, raising the question if top-1 error is the right performance measure. In this paper, we provide an extensive comparison and evaluation of established multiclass methods comparing their top-k performance both from a practical as well as from a theoretical perspective. Moreover, we introduce novel top-k loss functions as modifications of the softmax and the multiclass SVM losses and provide efficient optimization schemes for them. In the experiments, we compare on various datasets all of the proposed and established methods for top-k error optimization. An interesting insight of this paper is that the softmax loss yields competitive top-k performance for all k simultaneously. For a specific top-k error, our new top-k losses lead typically to further improvements while being faster to train than the softmax.

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs well on large-scale convex and non-convex optimization problems, exhibiting linear convergence and rapidly solving the optimization problems to high levels of precision. Furthermore, we show that our algorithm performs well for a wide-range of step sizes, often differing by several orders of magnitude.

In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_\lambda(\alpha, \beta) = \|Y - \alpha\mathbf{1} - X\beta\|_2^2 + p_{\lambda}(\beta)\] where $\alpha$ is the intercept which can be omitted depending on application; $\beta$ is the coefficients and $p_{\lambda}$ is the penalized function with penalizing parameter $\lambda$. $f_\lambda(\alpha, \beta)$ includes interesting classes such as Lasso, Ridge regression and Elastic-net. Compared to latest iterative distributed algorithms requiring multiple MapReduce jobs, our algorithm achieves huge performance improvement; moreover, our algorithm is exact compared to the approximate algorithms such as parallel stochastic gradient decent. Moreover, what our algorithm distinguishes with others is that it trains the model with cross validation to choose optimal $\lambda$ instead of user specified one. Key words: penalized linear regression, lasso, elastic-net, ridge, MapReduce

I know that CNN's are used a lot for computer vision where we want to deal with local features of the image. This makes sense because one pixel influences how we interpret its neighbours. If we had data for, say, medical decisions and we recorded many variables like age, weight, and existing medical conditions, these inputs have no distance between them and no sense of order which we could use to identify nearest neighbours. Having said that I could imagine that it might be useful to use a CNN for the inputs because it groups together inputs in ways which are unlikely to occur by chance if we just trained a NN by stochastic gradient descent.

Tree based learning algorithms are considered to be one of the best and mostly used supervised learning methods. Tree based methods empower predictive models with high accuracy, stability and ease of interpretation. Unlike linear models, they map non-linear relationships quite well. They are adaptable at solving any kind of problem at hand (classification or regression). Methods like decision trees, random forest, gradient boosting are being popularly used in all kinds of data science problems. Hence, for every analyst (fresher also), it's important to learn these algorithms and use them for modeling. This tutorial is meant to help beginners learn tree based modeling from scratch. After the successful completion of this tutorial, one is expected to become proficient at using tree based algorithms and build predictive models. Note: This tutorial requires no prior knowledge of machine learning.

Roughly a year and a half ago, I had the privelage of taking a graduate "Introduction to Machine Learning" course under the tutelage of the fantastic Professor Leslie Kaelbling. While I learned a great deal over the course of the semester, there was one minor point that she made to the class which stuck with me more than I expected it to at the time: before using a really fancy or sophisticated or "in-vogue" machine learning algorithm to solve your problem, try a simple Nearest Neighbor Search first. Let's say I gave you a bunch of data points, each with a location in space and a value, and then asked you to predict the value of a new point in space. Perhaps the values of you data are binary (just s and -s) and you've heard of Support Vector Machines. Should you give that a shot?