Bayesian Reasoning and Machine Learning by David Barber has a chapter on Approximate Sampling Christophe Andrieu et al. have written an introductory tutorial (pdf) on MCMC methods that covers most of the MCMC algorithms Dr. Daphne Koller offers an online course on Coursera, Probabilistic Graphical Models, which also covers the Gibbs Sampler and the Metropolis-Hastings Algorithm Dr. A. Taylan Cemgil has prepared very useful lecture notes (pdf) for his Monte Carlo methods course

According to the American Cancer Society, cancer kills more than 8 million people each year. Early detection can boost survival rates. Researchers and clinicians are feverishly exploring avenues to provide early and accurate diagnoses, as well as more targeted treatments. Blood screenings are used to detect many types of cancers, including liver, ovarian, colon and lung cancers. Current blood screening methods typically rely on affixing biochemical labels to cells or biomolecules.

Presbyterian reverend Thomas Bayes had no reason to suspect he'd make any lasting contribution to humankind. Born in England at the beginning of the 18th century, Bayes was a quiet and questioning man. He published only two works in his lifetime. In 1731, he wrote a defense of God's--and the British monarchy's--"divine benevolence," and in 1736, an anonymous defense of the logic of Isaac Newton's calculus. Yet an argument he wrote before his death in 1761 would shape the course of history.

We introduce a novel multivariate random process producing Bernoulli outputs per dimension, that can possibly formalize binary interactions in various graphical structures and can be used to model opinion dynamics, epidemics, financial and biological time series data, etc. We call this a Bernoulli Autoregressive Process (BAR). A BAR process models a discrete-time vector random sequence of $p$ scalar Bernoulli processes with autoregressive dynamics and corresponds to a particular Markov Chain. The benefit from the autoregressive dynamics is the description of a $2^p\times 2^p$ transition matrix by at most $pd$ effective parameters for some $d\ll p$ or by two sparse matrices of dimensions $p\times p^2$ and $p\times p$, respectively, parameterizing the transitions. Additionally, we show that the BAR process mixes rapidly, by proving that the mixing time is $O(\log p)$. The hidden constant in the previous mixing time bound depends explicitly on the values of the chain parameters and implicitly on the maximum allowed in-degree of a node in the corresponding graph. For a network with $p$ nodes, where each node has in-degree at most $d$ and corresponds to a scalar Bernoulli process generated by a BAR, we provide a greedy algorithm that can efficiently learn the structure of the underlying directed graph with a sample complexity proportional to the mixing time of the BAR process. The sample complexity of the proposed algorithm is nearly order-optimal as it is only a $\log p$ factor away from an information-theoretic lower bound. We present simulation results illustrating the performance of our algorithm in various setups, including a model for a biological signaling network.

We introduce a class of network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by permitting the location of a new edge to explicitly depend on the structure of the graph, but being nonetheless statistically and computationally tractable. In the limit of infinite walk length, the model converges to an extension of the preferential attachment model---in this sense, it can be motivated alternatively by asking what preferential attachment is an approximation to. Theoretical properties, including the limiting degree sequence, are studied analytically. If the entire history of the graph is observed, parameters can be estimated by maximum likelihood. If only the final graph is available, its history can be imputed using MCMC. We develop a class of sequential Monte Carlo algorithms that are more generally applicable to sequential random graph models, and may be of interest in their own right. The model parameters can be recovered from a single graph generated by the model. Applications to data clarify the role of the random walk length as a length scale of interactions within the graph.

A Graphical Model (GM) describes a probability distribution over a set of random variables which factorizes over the edges of a graph. It is of interest to recover the structure of GMs from random samples. The graphical structure contains valuable information on the dependencies between the random variables. In fact, the neighborhood of a random variable is the minimal set that provides us maximum information about this variable. Unsurprisingly, GM reconstruction plays an important role in various fields such as the study of gene expression [1], protein interactions [2], neuroscience [3], image processing [4], sociology [5] and even grid science [6, 7]. The origin of the GM reconstruction problem is traced back to the seminal 1968 paper by Chow and Liu [8], where the problem was posed and resolved for the special case of tree-structured GMs. In this special tree case the maximum likelihood estimator is tractable and is tantamount to finding a maximum weighted spanning-tree. However, it is also known that in the case of general graphs with cycles, maximum likelihood estimators are intractable as they require computation of the partition function of the underlying GM, with notable exceptions of the Gaussian GM, see for instance [9], and some other special cases, like planar Ising models without magnetic field [10]. 1 A lot of efforts in this field has focused on learning Ising models, which are the most general GMs over binary variables with pairwise interaction/factorization. Early attempts to learn the Ising model structure efficiently were heuristic, based on various mean-field approximations, e.g.

Within Machine Learning many tasks are - or can be reformulated as - classification tasks. In classification tasks we are trying to produce a model which can give the correlation between the input data and the class each input belongs to. This model is formed with the feature-values of the input-data. For example, the dataset contains datapoints belonging to the classes Apples, Pears and Oranges and based on the features of the datapoints (weight, color, size etc) we are trying to predict the class. We need some amount of training data to train the Classifier, i.e. form a correct model of the data.

In case you've been hanging out with the technology groundhog in its cave: we're in the midst of an AI spring. The past two years have seen a resurgence in excitement around our ability to model human-like intelligence in computer algorithms. This excitement has a number of catalysts, not least of which is the enabled application of deep neural networks to a multitude of fields by the advancement of Moore's law. For the average person, the AI spring is a period of unbridled excitement: your iPhone will transcribe your voicemails so you don't have to lift the phone to your ear, Facebook will translate the posts of the friends you made during that one summer in college in Puerto Rico, and your Alexa can tell you interesting trivia about Star Wars. But the life of a startup CEO is not so simple.

Data Science for IoT vs Classic Data Science: 10 Differences Enterprise AI insights from the AI Europe event in London Is it time to consider data in motion in your big data projects?

Pat Bagley is easily my favorite political cartoonist, period. For the politically aware in Utah, he is almost legendary, enjoying superstar status. I've been aware of him since I was a kid, and I always loved his cartoons. Not only does his artistic style appeal to me, he has a way of illustrating a situation in politics that explains it more clearly than a thousand words. His cartoons are humorous, though darkly so. And with every one, you can't help but feel he's had the last word.