Root Cause Analysis for Anomalies is challenging because of the trade-off between the accuracy and its explanatory friendliness, required for industrial applications. In this paper we propose a framework for simple and friendly RCA within the Bayesian regime under certain restrictions (that Hessian at the mode is diagonal, here referred to as \emph{separability}) imposed on the predictive posterior. We show that this assumption is satisfied for important base models, including Multinomal, Dirichlet-Multinomial and Naive Bayes. To demonstrate the usefulness of the framework, we embed it into the Bayesian Net and validate on web server error logs (real world data set).

This document aims to provide a review on learning with deep generative models (DGMs), which is an highly-active area in machine learning and more generally, artificial intelligence. This review is not meant to be a tutorial, but when necessary, we provide self-contained derivations for completeness. This review has two features. First, though there are different perspectives to classify DGMs, we choose to organize this review from the perspective of graphical modeling, because the learning methods for directed DGMs and undirected DGMs are fundamentally different. Second, we differentiate model definitions from model learning algorithms, since different learning algorithms can be applied to solve the learning problem on the same model, and an algorithm can be applied to learn different models. We thus separate model definition and model learning, with more emphasis on reviewing, differentiating and connecting different learning algorithms. We also discuss promising future research directions. This review is by no means comprehensive as the field is evolving rapidly. The authors apologize in advance for any missed papers and inaccuracies in descriptions. Corrections and comments are highly welcome.

In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.

Computational modeling of human multimodal language is an emerging research area in natural language processing spanning the language, visual and acoustic modalities. Comprehending multimodal language requires modeling not only the interactions within each modality (intra-modal interactions) but more importantly the interactions between modalities (cross-modal interactions). In this paper, we propose the Recurrent Multistage Fusion Network (RMFN) which decomposes the fusion problem into multiple stages, each of them focused on a subset of multimodal signals for specialized, effective fusion. Cross-modal interactions are modeled using this multistage fusion approach which builds upon intermediate representations of previous stages. Temporal and intra-modal interactions are modeled by integrating our proposed fusion approach with a system of recurrent neural networks. The RMFN displays state-of-the-art performance in modeling human multimodal language across three public datasets relating to multimodal sentiment analysis, emotion recognition, and speaker traits recognition. We provide visualizations to show that each stage of fusion focuses on a different subset of multimodal signals, learning increasingly discriminative multimodal representations.

We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction in gradient estimation for latent variable models: namely, that variance reduction involves eliminating or reducing Fourier coefficients that do not have degree 1. We then use this connection to develop low-variance unbiased gradient estimators for binary latent variable models such as sigmoid belief networks. The estimator is based upon properties of the noise operator from Boolean Fourier theory and involves a sample-dependent baseline added to the REINFORCE estimator in a way that keeps the estimator unbiased. The baseline can be plugged into existing gradient estimators for further variance reduction.

TheHidden Markov Model or HMM is all about learning sequences. A lot of the data that would be very useful for us to model is in sequences. Stock prices are sequences of prices. Language is a sequence of words. Credit scoring involves sequences of borrowing and repaying money, and we can use those sequences to predict whether or not you're going to default.

In the traditional framework of spectral learning of stochastic time series models, model parameters are estimated based on trajectories of fully recorded observations. However, real-world time series data often contain missing values, and worse, the distributions of missingness events over time are often not independent of the visible process. Recently, a spectral OOM learning algorithm for time series with missing data was introduced and proved to be consistent, albeit under quite strong conditions. Here we refine the algorithm and prove that the original strong conditions can be very much relaxed. We validate our theoretical findings by numerical experiments, showing that the algorithm can consistently handle missingness patterns whose dynamic interacts with the visible process.

The whirl of reinforcement learning started with the advent of AlphaGo by DeepMind, the AI system built to play the game Go. Since then, various companies have invested a great deal of time, energy, and research, and today reinforcement learning is one of the hot topics within Deep Learning. That said, most businesses are struggling to find use cases for reinforcement learning or ways to encompass it within their business logic. So far, it's been studied only in risk-free, observed, environments that are easy to simulate, which means that industries like finance, health, insurance, tech-consultancies are reluctant to risk their own money to explore its applications. What's more, the aspect of "risk factoring" within reinforcement learning puts a high strain on systems.

Are you looking at improving and extending the capabilities of your machine learning systems? ML is becoming increasingly pervasive in the modern data-driven world. It is used extensively across many fields, such as search engines, robotics, self-driving cars, and more. It is transforming the way businesses operate. Being able to understand the trends and patterns in complex data is critical to success.

Alzheimer's Disease (AD) is characterized by a cascade of biomarkers becoming abnormal, the pathophysiology of which is very complex and largely unknown. Event-based modeling (EBM) is a data-driven technique to estimate the sequence in which biomarkers for a disease become abnormal based on cross-sectional data. It can help in understanding the dynamics of disease progression and facilitate early diagnosis and prognosis. In this work we propose a novel discriminative approach to EBM, which is shown to be more accurate than existing state-of-the-art EBM methods. The method first estimates for each subject an approximate ordering of events. Subsequently, the central ordering over all subjects is estimated by fitting a generalized Mallows model to these approximate subject-specific orderings. We also introduce the concept of relative distance between events which helps in creating a disease progression timeline. Subsequently, we propose a method to stage subjects by placing them on the estimated disease progression timeline. We evaluated the proposed method on Alzheimer's Disease Neuroimaging Initiative (ADNI) data and compared the results with existing state-of-the-art EBM methods. We also performed extensive experiments on synthetic data simulating the progression of Alzheimer's disease. The event orderings obtained on ADNI data seem plausible and are in agreement with the current understanding of progression of AD. The proposed patient staging algorithm performed consistently better than that of state-of-the-art EBM methods. Event orderings obtained in simulation experiments were more accurate than those of other EBM methods and the estimated disease progression timeline was observed to correlate with the timeline of actual disease progression. The results of these experiments are encouraging and suggest that discriminative EBM is a promising approach to disease progression modeling.