Stochastic And-Or grammars (AOG) extend traditional stochastic grammars of language to model other types of data such as images and events. In this paper we propose a representation framework of stochastic AOGs that is agnostic to the type of the data being modeled and thus unifies various domain-specific AOGs. Many existing grammar formalisms and probabilistic models in natural language processing, computer vision, and machine learning can be seen as special cases of this framework. We also propose a domain-independent inference algorithm of stochastic context-free AOGs and show its tractability under a reasonable assumption. Furthermore, we provide two interpretations of stochastic context-free AOGs as a subset of probabilistic logic, which connects stochastic AOGs to the field of statistical relational learning and clarifies their relation with a few existing statistical relational models.

We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state quantization: The \textit{Markovian} type and the \textit{marginal} type. We propose a set of novel, relaxed sufficient conditions, ensuring strong and fully characterized pathwise convergence of these filters to the respective MMSE state estimator. In particular, for marginal state quantizations, we introduce the notion of \textit{conditional regularity of stochastic kernels}, which, to the best of our knowledge, constitutes the most relaxed condition proposed, under which asymptotic optimality of the respective grid based filters is guaranteed. Further, we extend our convergence results, including filtering of bounded and continuous functionals of the state, as well as recursive approximate state prediction. For both Markovian and marginal quantizations, the whole development of the respective grid based filters relies more on linear-algebraic techniques and less on measure theoretic arguments, making the presentation considerably shorter and technically simpler.

We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for \emph{successful change detection} with respect to the sample size $n_p, n_q$, the dimension of data $m$, and the number of changed edges $d$. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for $n_p = \Omega(d^2 \log \frac{m^2+m}{2})$ and $n_q = \Omega({n_p^2})$, with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to $\min(n_p, n_q) = \Omega(d^2 \log \frac{m^2+m}{2})$ when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.

Covariance Is 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Welcome to the natural language processing (NLP) edition of my "under-the-hood" series on AI (artificial intelligence) technology. Most major tech companies are announcing initiatives, introducing products (e.g., Amazon (NASDAQ:AMZN) with its Echo device and platform) or experiments in public (e.g., Microsoft's (NASDAQ:MSFT) Tay debacle). On Seeking Alpha (and I am sure in many other places as well), the topic of natural language processing seems to be confusing many people because they are not clear on what new technologies here can do and what they should expect from them in the immediate future. Even though I have touched on the subject before - e.g. on my explanation of IBM's (NYSE:IBM) Watson - I feel like I have not explained the specific topic of natural language processing comprehensively. There is a specific reason why the topic is getting so much attention and it has to do with the convergence of various subfields of computer science and statistics.

While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence. The past few years have seen major advances in many perception tasks using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. To achieve integrated intelligence that involves both perception and inference, it is naturally desirable to tightly integrate deep learning and Bayesian models within a principled probabilistic framework, which we call Bayesian deep learning. In this unified framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in return, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a general introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, and control. In this survey, we also discuss the relationship and differences between Bayesian deep learning and other related topics like Bayesian treatment of neural networks.

We investigate the task of building open domain, conversational dialogue systems based on large dialogue corpora using generative models. Generative models produce system responses that are autonomously generated word-by-word, opening up the possibility for realistic, flexible interactions. In support of this goal, we extend the recently proposed hierarchical recurrent encoder-decoder neural network to the dialogue domain, and demonstrate that this model is competitive with state-of-the-art neural language models and back-off n-gram models. We investigate the limitations of this and similar approaches, and show how its performance can be improved by bootstrapping the learning from a larger question-answer pair corpus and from pretrained word embeddings.

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, whose associated graphical model is a single loop network. The contribution of this paper is twofold. First, we introduce belief propagation for Gaussian reciprocal processes. Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.

There are five main schools of thought in machine learning, and each has its own master algorithm – a general-purpose learner that can in principle be applied to any domain. The symbolists have inverse deduction, the connectionists have backpropagation, the evolutionaries have genetic programming, the Bayesians have probabilistic inference, and the analogizers have support vector machines. What we really need, however, is a single algorithm combining the key features of all of them. In this webinar I will summarize the five paradigms and describe my work toward unifying them, including in particular Markov logic networks. I will conclude by speculating on the new applications that a universal learner will enable, and how society will change as a result.

The first step to before being able to do Image or audio analyses would be to extract relevant frames from the video streams in real time. This is crucial to a smart interactive device and requires extensive down sizing of the data to run the models on the features identified most relevant. One also needs the device to identify and react to certain events (owner coming home, break-in etc) through a frame by frame comparative analysis. Let us start with the event that there is a disturbance and the image frames and audio data is fed into the trained model to classify the event into pre-defined classes (simplest cast being intrusion vs non intrusion). Given a frame, let us start with the features that we would extract from it to first look for faces within the scenario and then if we find one, to match it with the available "registered" face repository. Given pictures of the home-owner/family, we will have an extensively pre trained model.