We design new algorithms for the combinatorial pure exploration problem in the multi-arm bandit framework. In this problem, we are given K distributions and a collection of subsets $\mathcal{V} \subset 2^K$ of these distributions, and we would like to find the subset $v \in \mathcal{V}$ that has largest cumulative mean, while collecting, in a sequential fashion, as few samples from the distributions as possible. We study both the fixed budget and fixed confidence settings, and our algorithms essentially achieve state-of-the-art performance in all settings, improving on previous guarantees for structures like matchings and submatrices that have large augmenting sets. Moreover, our algorithms can be implemented efficiently whenever the decision set V admits linear optimization. Our analysis involves precise concentration-of-measure arguments and a new algorithm for linear programming with exponentially many constraints.

Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and distributed systems such as compute clusters. Recent work has proposed running iterative algorithms such as gradient descent and MCMC in parallel asynchronously for increased performance, with good empirical results in certain problems. Unfortunately, for MCMC this parallelization technique requires new convergence theory, as it has been explicitly demonstrated to lead to divergence on some examples. Recent theory on Asynchronous Gibbs sampling describes why these algorithms can fail, and provides a way to alter them to make them converge. In this article, we describe how to apply this theory in a generic setting, to understand the asynchronous behavior of any MCMC algorithm, including those implemented using parameter servers, and those not based on Gibbs sampling.

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling.

We consider the problem of universal joint clustering and registration of images and define algorithms using multivariate information functionals. We first study registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi-image registration, and design an asymptotically optimal algorithm based on multiinformation. Further, we define a novel multivariate information functional to perform joint clustering and registration of images, and prove consistency of the algorithm. Finally, we consider registration and clustering of numerous limited-resolution images, defining algorithms that are order-optimal in scaling of number of pixels in each image with the number of images.

Large data collections required for the training of neural networks often contain sensitive information such as the medical histories of patients, and the privacy of the training data must be preserved. In this paper, we introduce a dropout technique that provides an elegant Bayesian interpretation to dropout, and show that the intrinsic noise added, with the primary goal of regularization, can be exploited to obtain a degree of differential privacy. The iterative nature of training neural networks presents a challenge for privacy-preserving estimation since multiple iterations increase the amount of noise added. We overcome this by using a relaxed notion of differential privacy, called concentrated differential privacy, which provides tighter estimates on the overall privacy loss. We demonstrate the accuracy of our privacy-preserving dropout algorithm on benchmark datasets.

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data. Some of the most successful approaches have used probabilistic models to uncover latent thematic structure in discrete data. Despite the success of these models on textual data, they have not generalized as well to image data, in part because of the spatial and temporal structure that may exist in an image stream. We introduce a novel unsupervised machine learning framework that incorporates the ability of convolutional autoencoders to discover features from images that directly encode spatial information, within a Bayesian nonparametric topic model that discovers meaningful latent patterns within discrete data. By using this hybrid framework, we overcome the fundamental dependency of traditional topic models on rigidly hand-coded data representations, while simultaneously encoding spatial dependency in our topics without adding model complexity. We apply this model to the motivating application of high-level scene understanding and mission summarization for exploratory marine robots. Our experiments on a seafloor dataset collected by a marine robot show that the proposed hybrid framework outperforms current state-of-the-art approaches on the task of unsupervised seafloor terrain characterization.

When I was beginning my way in data science, I often faced the problem of choosing the most appropriate algorithm for my specific problem. If you're like me, when you open some article about Machine Learning algorithms, you see dozens of detailed descriptions. The paradox is that they don't ease the choice. In this article, I will try to explain basic concepts and give some intuition of using different kinds of Machine Learning algorithms in different tasks. At the end of the article, you'll find the structured overview of the main features of described algorithms.

We find that the variable Dependents has a level 3 which shall be treated too. It's quite simple to modify the name levels in a factor variable.

The problem descriptions are taken straightaway from the assignments. In this assignment a linear classifier will be implemented and it will be trained using stochastic gradient descent with numpy. To make things more intuitive, let's solve a 2D classification problem with synthetic data. As we can notice the data above isn't linearly separable. Hence we should add features(or use non-linear model). Note that decision line between two classes have form of circle, since that we can add quadratic features to make the problem linearly separable.

Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the microscopic structure, such as the first-and second-order proximity of vertexes, while the macroscopic scale-free property is largely ignored. Scale-free property depicts the fact that vertex degrees follow a heavy-tailed distribution (i.e., only a few vertexes have high degrees) and is a critical property of real-world networks, such as social networks. In this paper, we study the problem of learning representations for scale-free networks. We first theoretically analyze the difficulty of embedding and reconstructing a scale-free network in the Euclidean space, by converting our problem to the sphere packing problem. Then, we propose the "degree penalty" principle for designing scale-free property preserving network embedding algorithm: punishing the proximity between high-degree vertexes. We introduce two implementations of our principle by utilizing the spectral techniques and a skip-gram model respectively. Extensive experiments on six datasets show that our algorithms are able to not only reconstruct heavy-tailed distributed degree distribution, but also outperform state-of- the-art embedding models in various network mining tasks, such as vertex classification and link prediction. 1 Introduction Network analysis has attracted considerable research efforts in many areas of artificial intelligence, as networks are able to encode rich and complex data, such as human relationships and interactions. One major challenge of network analysis is how to represent network properly so that the network structure can be preserved.