We consider a decision-making problem where the environment varies both in space and time. Such problems arise naturally when considering e.g., the navigation of an underwater robot amidst ocean currents or the navigation of an aerial vehicle in wind. To model such spatiotemporal variation, we extend the standard Markov Decision Process (MDP) to a new framework called the Time-Varying Markov Decision Process (TVMDP). The TVMDP has a time-varying state transition model and transforms the standard MDP that considers only immediate and static uncertainty descriptions of state transitions, to a framework that is able to adapt to future time-varying transition dynamics over some horizon. We show how to solve a TVMDP via a redesign of the MDP value propagation mechanisms by incorporating the introduced dynamics along the temporal dimension. We validate our framework in a marine robotics navigation setting using spatiotemporal ocean data and show that it outperforms prior efforts.

Consider a multi-variate time series $(X_t)_{t=0}^{T}$ where $X_t \in \mathbb{R}^d$ which may represent spike train responses for multiple neurons in a brain, crime event data across multiple regions, and many others. An important challenge associated with these time series models is to estimate an influence network between the $d$ variables, especially when the number of variables $d$ is large meaning we are in the high-dimensional setting. Prior work has focused on parametric vector auto-regressive models. However, parametric approaches are somewhat restrictive in practice. In this paper, we use the non-parametric sparse additive model (SpAM) framework to address this challenge. Using a combination of $\beta$ and $\phi$-mixing properties of Markov chains and empirical process techniques for reproducing kernel Hilbert spaces (RKHSs), we provide upper bounds on mean-squared error in terms of the sparsity $s$, logarithm of the dimension $\log d$, number of time points $T$, and the smoothness of the RKHSs. Our rates are sharp up to logarithm factors in many cases. We also provide numerical experiments that support our theoretical results and display potential advantages of using our non-parametric SpAM framework for a Chicago crime dataset.

Data association, the reasoning over correspondence between targets and measurements, is a problem of fundamental importance in target tracking. Recently, belief propagation (BP) has emerged as a promising method for estimating the marginal probabilities of measurement to target association, providing fast, accurate estimates. The excellent performance of BP in the particular formulation used may be attributed to the convexity of the underlying free energy which it implicitly optimises. This paper studies multiple scan data association problems, i.e., problems that reason over correspondence between targets and several sets of measurements, which may correspond to different sensors or different time steps. We find that the multiple scan extension of the single scan BP formulation is non-convex and demonstrate the undesirable behaviour that can result. A convex free energy is constructed using the recently proposed fractional free energy (FFE). A convergent, BP-like algorithm is provided for the single scan FFE, and employed in optimising the multiple scan free energy using primal-dual coordinate ascent. Finally, based on a variational interpretation of joint probabilistic data association (JPDA), we develop a sequential variant of the algorithm that is similar to JPDA, but retains consistency constraints from prior scans. The performance of the proposed methods is demonstrated on a bearings only target localisation problem.

In this article a few simple applications of Markov chain are going to be discussed as a solution to a few text processing problems. These problems appeared as assignments in a few courses, the descriptions are taken straightaway from the courses themselves. Use a Markov chain to create a statistical model of a piece of English text. Simulate the Markov chain to generate stylized pseudo-random text. In the 1948 landmark paper A Mathematical Theory of Communication, Claude Shannon founded the field of information theory and revolutionized the telecommunications industry, laying the groundwork for today's Information Age. In this paper, Shannon proposed using a Markov chain to create a statistical model of the sequences of letters in a piece of English text. Markov chains are now widely used in speech recognition, handwriting recognition, information retrieval, data compression, and spam filtering. They also have many scientific computing applications including the genemark algorithm for gene prediction, the Metropolis algorithm for measuring thermodynamical properties, and Google's PageRank algorithm for Web search.

In this article a few simple applications of Markov chain are going to be discussed as a solution to a few text processing problems. These problems appeared as assignments in a few courses, the descriptions are taken straightaway from the courses themselves. Use a Markov chain to create a statistical model of a piece of English text. Simulate the Markov chain to generate stylized pseudo-random text. In the 1948 landmark paper A Mathematical Theory of Communication, Claude Shannon founded the field of information theory and revolutionized the telecommunications industry, laying the groundwork for today's Information Age. In this paper, Shannon proposed using a Markov chain to create a statistical model of the sequences of letters in a piece of English text. Markov chains are now widely used in speech recognition, handwriting recognition, information retrieval, data compression, and spam filtering. They also have many scientific computing applications including the genemark algorithm for gene prediction, the Metropolis algorithm for measuring thermodynamical properties, and Google's PageRank algorithm for Web search.

Neural network based architectures used for sound recognition are usually adapted from other application domains such as image recognition, which may not harness the time-frequency representation of a signal. The ConditionaL Neural Networks (CLNN) and its extension the Masked ConditionaL Neural Networks (MCLNN) are designed for multidimensional temporal signal recognition. The CLNN is trained over a window of frames to preserve the inter-frame relation, and the MCLNN enforces a systematic sparseness over the network's links that mimics a filterbank-like behavior. The masking operation induces the network to learn in frequency bands, which decreases the network susceptibility to frequency-shifts in time-frequency representations. Additionally, the mask allows an exploration of a range of feature combinations concurrently analogous to the manual handcrafting of the optimum collection of features for a recognition task. MCLNN have achieved competitive performance on the Ballroom music dataset compared to several hand-crafted attempts and outperformed models based on state-of-the-art Convolutional Neural Networks.

Currently, many of us are overwhelmed with mighty power of Deep Learning. We start to forget about humble graphical models. CRF is not so trendy as LSTM, but it is robust, reliable and worth noting. In this post, you will find a short summary about CRF (aka Conditional Random Fields) – what is this thing, what is it for and some interesting facts. In practical implementation, the computational time is often larger due to many other operations like numerical scaling, smoothing etc.

GANs were introduced by Ian Goodfellow in 2014. Both of them are dedicated to extract features from data by learning the identity function f(x) x and both of them rely on Markov chains to train or to generate samples. Generative adversarial networks were designed to avoid using Markov chains because of the high computational cost of the latter. Another advantage relative to Boltzmann machines is that the Generator function has much fewer restrictions (there are only a few probability distributions that admit Markov chain sampling). In this article, we'll tell you how generative adversarial nets work and what their most popular applications in real life are.

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. The generalized form of the noisy expectation-maximization (NEM) algorithm allow for arbitrary modes of noise injection including adding and multiplying noise to the data. We demonstrate these noise benefits on EM algorithms for the Gaussian mixture model (GMM) with both additive and multiplicative NEM noise injection. A separate theorem (not presented here) shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse. Injecting blind noise only slowed convergence.

With the release of Apple's Siri and comparable voice search assistance from Microsoft and Google, you might have speculated why it took so long for speech recognition innovation to progress to this stage. In addition, one may also wonder what the future holds for natural language-based machine intelligence learning and its impact on our everyday lives. A closer look at the history and development of voice recognition technology may be somewhat akin to watching a toddler grow up, advancing from the baby-talk level and developing terminologies of countless words to responding to queries with fast, amusing repartees, just like what the clever digital assistant Siri does. Here is a close depiction at the innovations of the past generations with regards to speech recognition and what the future has in store for this technology. The "Audrey" system is the earliest speech recognition device that could recognize only digits.