We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

We propose a framework for modeling and estimating the state of controlled dynamical systems, where an agent can affect the system through actions and receives partial observations. Based on this framework, we propose the Predictive State Representation with Random Fourier Features (RFFPSR). A key property in RFF-PSRs is that the state estimate is represented by a conditional distribution of future observations given future actions. RFF-PSRs combine this representation with moment-matching, kernel embedding and local optimization to achieve a method that enjoys several favorable qualities: It can represent controlled environments which can be affected by actions; it has an efficient and theoretically justified learning algorithm; it uses a non-parametric representation that has expressive power to represent continuous non-linear dynamics. We provide a detailed formulation, a theoretical analysis and an experimental evaluation that demonstrates the effectiveness of our method.

In this article I revisit the learned material from the amazing machine learning course by Andre Ng on coursera and create an overview about the concepts. All quotes refer to the material from the course if not explicitly stated otherwise. Linear regression tries to fit points to a line generated by an algorithm. This optimized line (the model) is capable of predicting values for certain input values and can be plotted. We want to set the parameters in order to achieve a minimal difference between the predicted and the real values.

In part one of the machine learning crash course, we introduced the field of supervised machine learning (ML) by walking through popular algorithms like linear regression and logistic regression. But supervised learning is just one of the many types of algorithms in the vast machine learning / artificial intelligence space. In this article, we take a look at two other subdisciplines: Unsupervised learning and deep learning. When performing supervised learning, our datasets consisted of labeled examples. In the linear regression example, we had TV advertising data labeled with the amount of sales generated.

In machine learning, there's something called the "No Free Lunch" theorem. In a nutshell, it states that no one algorithm works best for every problem, and it's especially relevant for supervised learning (i.e. For example, you can't say that neural networks are always better than decision trees or vice-versa. There are many factors at play, such as the size and structure of your dataset. As a result, you should try many different algorithms for your problem, while using a hold-out "test set" of data to evaluate performance and select the winner.

This is the sixth part of "An Outsider's Tour of Reinforcement Learning." Our first generic candidate for solving reinforcement learning is Policy Gradient. I find it shocking that Policy Gradient wasn't ruled out as a bad idea in 1993. Policy gradient is seductive as it apparently lets one fine tune a program to solve any problem without any domain knowledge. Of course, anything that makes such a claim must be too general for its own good.

In a February 6 blog, I discussed the unsupervised machine learning Naive Bayes algorithm with an example that was hopefully easy to understand for beginners. During the summer of 2017, I began a five-part series on types of machine learning. That series included more details about k-Nearest neighbor, K-means clustering, Singular Value Decomposition, Principal Component Analysis, Apriori, Frequent Pattern-Growth and more. Today I want to expand on the ideas presented in my Support Vector "Data Science in 90 Seconds" YouTube video and continue the discussion in plain language. If you recall from earlier discussions, supervised machine learning is the'task of inferring a function to describe hidden structure from labeled data'.

An approximate method for conducting resampling in Lasso, the $\ell_1$ penalized linear regression, in a semi-analytic manner is developed, whereby the average over the resampled datasets is directly computed without repeated numerical sampling, thus enabling an inference free of the statistical fluctuations due to sampling finiteness, as well as a significant reduction of computational time. The proposed method is employed to implement bootstrapped Lasso (Bolasso) and stability selection, both of which are variable selection methods using resampling in conjunction with Lasso, and it resolves their disadvantage regarding computational cost. To examine approximation accuracy and efficiency, numerical experiments were carried out using simulated datasets. Moreover, an application to a real-world dataset, the wine quality dataset, is presented. To process such real-world datasets, an objective criterion for determining the relevance of selected variables is also introduced by the addition of noise variables and resampling.

Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.

We propose a new active learning strategy designed for deep neural networks. The goal is to minimize the number of data annotation queried from an oracle during training. Previous active learning strategies scalable for deep networks were mostly based on uncertain sample selection. In this work, we focus on examples lying close to the decision boundary. Based on theoretical works on margin theory for active learning, we know that such examples may help to considerably decrease the number of annotations. While measuring the exact distance to the decision boundaries is intractable, we propose to rely on adversarial examples. We do not consider anymore them as a threat instead we exploit the information they provide on the distribution of the input space in order to approximate the distance to decision boundaries. We demonstrate empirically that adversarial active queries yield faster convergence of CNNs trained on MNIST, the Shoe-Bag and the Quick-Draw datasets.