Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure called globally sparse probabilistic PCA (GSPPCA) that allows to obtain several sparse components with the same sparsity pattern. This allows the practitioner to identify the original variables which are relevant to describe the data. To this end, using Roweis' probabilistic interpretation of PCA and a Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. To avoid the drawbacks of discrete model selection, a simple relaxation of this framework is presented. It allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood is then maximized over this path. This approach is illustrated on real and synthetic data sets. In particular, using unlabeled microarray data, GSPPCA infers much more relevant gene subsets than traditional sparse PCA algorithms.

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remarkable result: despite the non-convexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of non-convex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber & Candes (2015) to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for non-convex optimization and a novel way of exploiting non-convexity for statistical inference.

In this paper we study a model-based approach to calculating approximately optimal policies in Markovian Decision Processes. In particular, we derive novel bounds on the loss of using a policy derived from a factored linear model, a class of models which generalize numerous previous models out of those that come with strong computational guarantees. For the first time in the literature, we derive performance bounds for model-based techniques where the model inaccuracy is measured in weighted norms. Moreover, our bounds show a decreased sensitivity to the discount factor and, unlike similar bounds derived for other approaches, they are insensitive to measure mismatch. Similarly to previous works, our proofs are also based on contraction arguments, but with the main differences that we use carefully constructed norms building on Banach lattices, and the contraction property is only assumed for operators acting on "compressed" spaces, thus weakening previous assumptions, while strengthening previous results.

The prescribed viewpoint appears to be good enough to accommodate most of the existing spectral graph techniques as a consequence of just one single formalism and algorithm. Keywords and phrases: Nonparametric spectral graph analysis; Graph correlation density field (GraField); Empirical and smoothed spectral graph analysis; High-dimensional discrete data smoothing.

We introduce a new artificial intelligence (AI) approach called, the 'Digital Synaptic Neural Substrate' (DSNS). It uses selected attributes from objects in various domains (e.g. chess problems, classical music, renowned artworks) and recombines them in such a way as to generate new attributes that can then, in principle, be used to create novel objects of creative value to humans relating to any one of the source domains. This allows some of the burden of creative content generation to be passed from humans to machines. The approach was tested in the domain of chess problem composition. We used it to automatically compose numerous sets of chess problems based on attributes extracted and recombined from chess problems and tournament games by humans, renowned paintings, computer-evolved abstract art, photographs of people, and classical music tracks. The quality of these generated chess problems was then assessed automatically using an existing and experimentally-validated computational chess aesthetics model. They were also assessed by human experts in the domain. The results suggest that attributes collected and recombined from chess and other domains using the DSNS approach can indeed be used to automatically generate chess problems of reasonably high aesthetic quality. In particular, a low quality chess source (i.e. tournament game sequences between weak players) used in combination with actual photographs of people was able to produce three-move chess problems of comparable quality or better to those generated using a high quality chess source (i.e. published compositions by human experts), and more efficiently as well. Why information from a foreign domain can be integrated and functional in this way remains an open question for now. The DSNS approach is, in principle, scalable and applicable to any domain in which objects have attributes that can be represented using real numbers.

Composition conventions are guidelines used by human composers in composing chess problems. They are particularly significant in composition tournaments. Examples include, not having any check in the first move of the solution and not dressing up the board with unnecessary pieces. Conventions are often associated or even directly conflated with the overall aesthetics or beauty of a composition. Using an existing experimentally-validated computational aesthetics model for three-move mate problems, we analyzed sets of computer-generated compositions adhering to at least 2, 3 and 4 comparable conventions to test if simply conforming to more conventions had a positive effect on their aesthetics, as is generally believed by human composers. We found slight but statistically significant evidence that it does, but only to a point. We also analyzed human judge scores of 145 three-move mate problems composed by humans to see if they had any positive correlation with the computational aesthetic scores of those problems. We found that they did not. These seemingly conflicting findings suggest two main things. First, the right amount of adherence to composition conventions in a composition has a positive effect on its perceived aesthetics. Second, human judges either do not look at the same conventions related to aesthetics in the model used or emphasize others that have less to do with beauty as perceived by the majority of players, even though they may mistakenly consider their judgements beautiful in the traditional, non-esoteric sense. Human judges may also be relying significantly on personal tastes as we found no correlation between their individual scores either.

A framework for consensus modelling is introduced using Kleene's three valued logic as a means to express vagueness in agents' beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a propositional language may be absolutely true, absolutely false or borderline. By exploiting these intermediate truth values, we can allow agents to adopt a more vague interpretation of underlying concepts in order to weaken their beliefs and reduce the levels of inconsistency, so as to achieve consensus. We consider a consensus combination operation which results in agents adopting the borderline truth value as a shared viewpoint if they are in direct conflict. Simulation experiments are presented which show that applying this operator to agents chosen at random (subject to a consistency threshold) from a population, with initially diverse opinions, results in convergence to a smaller set of more precise shared beliefs. Furthermore, if the choice of agents for combination is dependent on the payoff of their beliefs, this acting as a proxy for performance or usefulness, then the system converges to beliefs which, on average, have higher payoff.

Rami Malek said it better than anyone: "Please tell me you're seeing this, too." It was a reference to his Mr. Robot character Elliot's tenuous grip on reality, but as he stood there accepting his Emmy for Outstanding Lead Actor in a Drama Series, it was also the phrase so many viewers had to be whispering to themselves for hours. Throughout last night's telecast, underdogs like Orphan Black's Tatiana Maslany actually won, TV's growing diversity was celebrated (take that, Oscars), and streaming services proved their method of shaking up the TV model was working by scoring scads of trophies. It felt like a dream. Sure, Jimmy Kimmel wasn't the best host, and there was a sense of immobility at the top, as HBO's Veep and Game of Thrones took home Outstanding Comedy Series and Outstanding Drama Series, respectively, for the second year in a row.

The global cognitive computing market is expected to reach 12.5 billion in 2019, up from 2.5 billion in 2014, at a CAGR of 38%. Cognitive computing is another way of describing machine learning, an area of computer science which sees machines recognizing patterns and learning new material -- without being explicitly programmed by a human. As more businesses identify benefits of cognitive computing, the machine learning market is growing. Possible applications of machine learning are vast and varied. A survey from 451 Research outlines future initiatives that will impact the growth, use of, and quality of data under management, which is a critical component of machine learning and AI. Additionally, the report defined use cases that enterprises consider for employing machine learning.

By 2021, robots will have eliminated 6% of all jobs in the US, starting with customer service representatives and eventually truck and taxi drivers. That's just one cheery takeaway from a report released by market research company Forrester this week. These robots, or intelligent agents, represent a set of AI-powered systems that can understand human behavior and make decisions on our behalf. Current technologies in this field include virtual assistants like Alexa, Cortana, Siri and Google Now as well as chatbots and automated robotic systems. For now, they are quite simple, but over the next five years they will become much better at making decisions on our behalf in more complex scenarios, which will enable mass adoption of breakthroughs like self-driving cars.