We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\ell_p$-norm TV. The most important among these is $\ell_1$-norm TV, for whose prox-operator we present a new geometric analysis which unveils a hitherto unknown connection to taut-string methods. This connection turns out to be remarkably useful as it shows how our geometry guided implementation results in efficient weighted and unweighted 1D-TV solvers, surpassing state-of-the-art methods. Our 1D-TV solvers provide the backbone for building more complex (two or higher-dimensional) TV solvers within a modular proximal optimization approach. We review the literature for an array of methods exploiting this strategy, and illustrate the benefits of our modular design through extensive suite of experiments on (i) image denoising, (ii) image deconvolution, (iii) four variants of fused-lasso, and (iv) video denoising. To underscore our claims and permit easy reproducibility, we provide all the reviewed and our new TV solvers in an easy to use multi-threaded C++, Matlab and Python library.

After finishing Udacity Deep Learning Foundation I felt that I got a good introduction to Deep Learning, but to understand things, I must dig deeper. Besides I had a guaranteed admission to Self-Driving Car Engineer, Artificial Intelligence, or Robotics Nanodegree programs. Before I turn to Udacity advanced courses, I want to mention one thing at the beginning. If I could give advice to myself, I would select another introduction course on Deep Learning -- Deep Learning Specialization by Andrew Ng. First of all, his way of mentoring is unique and he can explain complex things in most clear and understandable way.

A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which are encoded by class labels. Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.

Learning probability distributions on the weights of neural networks (NNs) has recently proven beneficial in many applications. Bayesian methods, such as Stein variational gradient descent (SVGD), offer an elegant framework to reason about NN model uncertainty. However, by assuming independent Gaussian priors for the individual NN weights (as often applied), SVGD does not impose prior knowledge that there is often structural information (dependence) among weights. We propose efficient posterior learning of structural weight uncertainty, within an SVGD framework, by employing matrix variate Gaussian priors on NN parameters. We further investigate the learned structural uncertainty in sequential decision-making problems, including contextual bandits and reinforcement learning. Experiments on several synthetic and real datasets indicate the superiority of our model, compared with state-of-the-art methods.

To assure cyber security of an enterprise, typically SIEM (Security Information and Event Management) system is in place to normalize security event from different preventive technologies and flag alerts. Analysts in the security operation center (SOC) investigate the alerts to decide if it is truly malicious or not. However, generally the number of alerts is overwhelming with majority of them being false positive and exceeding the SOC's capacity to handle all alerts. There is a great need to reduce the false positive rate as much as possible. While most previous research focused on network intrusion detection, we focus on risk detection and propose an intelligent Deep Belief Network machine learning system. The system leverages alert information, various security logs and analysts' investigation results in a real enterprise environment to flag hosts that have high likelihood of being compromised. Text mining and graph based method are used to generate targets and create features for machine learning. In the experiment, Deep Belief Network is compared with other machine learning algorithms, including multi-layer neural network, random forest, support vector machine and logistic regression. Results on real enterprise data indicate that the deep belief network machine learning system performs better than other algorithms for our problem and is six times more effective than current rule-based system. We also implement the whole system from data collection, label creation, feature engineering to host score generation in a real enterprise production environment.

This article aims to take on a few of the machine learning algorithms for people who aim to gain knowledge on important machine learning concepts while using freely available materials and resources along the way. The prime objective of this outline is to help you wade through the numerous free options that are available. There are many, to be sure, but which are the best? What is the best order in which to use selected resources? Below are the common machine learning Algorithms briefly explained with Python and R code.

Remarkably general method for bounding the statistical risk of penalized likelihood estimators comes from work on two-part coding, one of the minimum description length (MDL) approaches to statistical inference. Two-part coding MDL prescribes assigning codelengths to a model (or model class) then selecting the distribution that provides the most efficient description of one's data [1]. The total description length has two parts: the part that specifies a distribution within the model (as well as a model within the model class if necessary) and the part that specifies the data with reference to the specified distribution. If the codelengths are exactly Kraft-valid, this approach is equivalent to Bayesian maximum a posteriori (MAP) estimation, in that the two parts correspond to log reciprocal of prior and log reciprocal of likelihood respectively. More generally, one can call the part of the codelength specifying the distribution a penalty term; it is called the complexity in MDL literature. Let (Θ, L) denote a discrete set indexing distributions along with a complexity function. With X P, the (pointwise) redundancy of any θ Θ is its two-part codelength minus log(1/p(X)), the codelength one gets by using P as the coding distribution.

Artificial intelligence (AI) generally and machine learning (ML) specifically demonstrate impressive practical success in many different application domains, e.g. in autonomous driving, speech recognition, or recommender systems. Deep learning approaches, trained on extremely large data sets or using reinforcement learning methods have even exceeded human performance in visual tasks, particularly on playing games such as Atari, or mastering the game of Go. Even in the medical domain there are remarkable results. The central problem of such models is that they are regarded as black-box models and even if we understand the underlying mathematical principles, they lack an explicit declarative knowledge representation, hence have difficulty in generating the underlying explanatory structures. This calls for systems enabling to make decisions transparent, understandable and explainable. A huge motivation for our approach are rising legal and privacy aspects. The new European General Data Protection Regulation entering into force on May 25th 2018, will make black-box approaches difficult to use in business. This does not imply a ban on automatic learning approaches or an obligation to explain everything all the time, however, there must be a possibility to make the results re-traceable on demand. In this paper we outline some of our research topics in the context of the relatively new area of explainable-AI with a focus on the application in medicine, which is a very special domain. This is due to the fact that medical professionals are working mostly with distributed heterogeneous and complex sources of data. In this paper we concentrate on three sources: images, *omics data and text. We argue that research in explainable-AI would generally help to facilitate the implementation of AI/ML in the medical domain, and specifically help to facilitate transparency and trust.

Automated seizure detection using clinical electroencephalograms is a challenging machine learning problem because the multichannel signal often has an extremely low signal to noise ratio. Events of interest such as seizures are easily confused with signal artifacts (e.g, eye movements) or benign variants (e.g., slowing). Commercially available systems suffer from unacceptably high false alarm rates. Deep learning algorithms that employ high dimensional models have not previously been effective due to the lack of big data resources. In this paper, we use the TUH EEG Seizure Corpus to evaluate a variety of hybrid deep structures including Convolutional Neural Networks and Long Short-Term Memory Networks. We introduce a novel recurrent convolutional architecture that delivers 30% sensitivity at 7 false alarms per 24 hours. We have also evaluated our system on a held-out evaluation set based on the Duke University Seizure Corpus and demonstrate that performance trends are similar to the TUH EEG Seizure Corpus. This is a significant finding because the Duke corpus was collected with different instrumentation and at different hospitals. Our work shows that deep learning architectures that integrate spatial and temporal contexts are critical to achieving state of the art performance and will enable a new generation of clinically-acceptable technology.

Objective: A clinical decision support tool that automatically interprets EEGs can reduce time to diagnosis and enhance real-time applications such as ICU monitoring. Clinicians have indicated that a sensitivity of 95% with a specificity below 5% was the minimum requirement for clinical acceptance. We propose a highperformance classification system based on principles of big data and machine learning. Methods: A hybrid machine learning system that uses hidden Markov models (HMM) for sequential decoding and deep learning networks for postprocessing is proposed. These algorithms were trained and evaluated using the TUH EEG Corpus, which is the world's largest publicly available database of clinical EEG data. Results: Our approach delivers a sensitivity above 90% while maintaining a specificity below 5%. This system detects three events of clinical interest: (1) spike and/or sharp waves, (2) periodic lateralized epileptiform discharges, (3) generalized periodic epileptiform discharges. It also detects three events used to model background noise: (1) artifacts, (2) eye movement (3) background. Conclusions: A hybrid HMM/deep learning system can deliver a low false alarm rate on EEG event detection, making automated analysis a viable option for clinicians. Significance: The TUH EEG Corpus enables application of highly data consumptive machine learning algorithms to EEG analysis. Performance is approaching clinical acceptance for real-time applications.