Artificial intelligence (AI) is intelligence exhibited by machines. In computer science, an ideal "intelligent" machine is a flexible rational agent that perceives its environment and takes actions that maximize its chance of success at some goal.[1] Colloquially, the term "artificial intelligence" is applied when a machine mimics "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving".[2] As machines become increasingly capable, facilities once thought to require intelligence are removed from the definition. For example, optical character recognition is no longer perceived as an exemplar of "artificial intelligence" having become a routine technology.[3] Capabilities still classified as AI include advanced Chess and Go systems and self-driving cars. AI research is divided into subfields[4] that focus on specific problems or on specific approaches or on the use of a particular tool or towards satisfying particular applications. The central problems (or goals) of AI research include reasoning, knowledge, planning, learning, natural language processing (communication), perception and the ability to move and manipulate objects.[5] General intelligence is among the field's long-term goals.[6] Approaches include statistical methods, computational intelligence, soft computing (e.g. machine learning), and traditional symbolic AI. Many tools are used in AI, including versions of search and mathematical optimization, logic, methods based on probability and economics. The AI field draws upon computer science, mathematics, psychology, linguistics, philosophy, neuroscience and artificial psychology. The field was founded on the claim that human intelligence "can be so precisely described that a machine can be made to simulate it."[7] This raises philosophical arguments about the nature of the mind and the ethics of creating artificial beings endowed with human-like intelligence, issues which have been explored by myth, fiction and philosophy since antiquity.[8] Attempts to create artificial intelligence has experienced many setbacks, including the ALPAC report of 1966, the abandonment of perceptrons in 1970, the Lighthill Report of 1973 and the collapse of the Lisp machine market in 1987. In the twenty-first century AI techniques became an essential part of the technology industry, helping to solve many challenging problems in computer science.[9]

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un- known (latent) variables is high. This is the setting in many problems in com- putational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse prob- lems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, is a formidable task. The goal of the present paper is two- fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors, and on the other, to ex- tend our work in [1] with regards to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the model proposed by employing Importance Sam- pling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical di- agnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

In cargo logistics, a key performance measure is transport risk, defined as the deviation of the actual arrival time from the planned arrival time. Neither earliness nor tardiness is desirable for customer and freight forwarders. In this paper, we investigate ways to assess and forecast transport risks using a half-year of air cargo data, provided by a leading forwarder on 1336 routes served by 20 airlines. Interestingly, our preliminary data analysis shows a strong multimodal feature in the transport risks, driven by unobserved events, such as cargo missing flights. To accommodate this feature, we introduce a Bayesian nonparametric model -- the probit stick-breaking process (PSBP) mixture model -- for flexible estimation of the conditional (i.e., state-dependent) density function of transport risk. We demonstrate that using simpler methods, such as OLS linear regression, can lead to misleading inferences. Our model provides a tool for the forwarder to offer customized price and service quotes. It can also generate baseline airline performance to enable fair supplier evaluation. Furthermore, the method allows us to separate recurrent risks from disruption risks. This is important, because hedging strategies for these two kinds of risks are often drastically different.

The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(\sqrt{T/p})$ and $O(\sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as \emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge.

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the number of observations is large, there exist many well developed approaches. Recently, high dimensional low sample size problems are becoming increasingly popular. Margin-based classifiers, such as logistic regression, are well established methods in the literature. On the other hand, in terms of probability estimation, it is known that for binary classifiers, the commonly used methods tend to under-estimate the norm of the classification function. This can lead to biased probability estimation. Remedy approaches have been proposed in the literature. However, for the simultaneous multicategory classification framework, much less work has been done. We fill the gap in this paper. In particular, we give theoretical insights on why heavy regularization terms are often needed in high dimensional applications, and how this can lead to bias in probability estimation. To overcome this difficulty, we propose a new refit strategy for multicategory angle-based classifiers. Our new method only adds a small computation cost to the problem, and is able to attain prediction accuracy that is as good as the regular margin-based classifiers. On the other hand, the improvement of probability estimation can be very significant. Numerical results suggest that the new refit approach is highly competitive.

Summary: I describe how the TrueSkill algorithm works using concepts you're already familiar with. TrueSkill is used on Xbox Live to rank and match players and it serves as a great way to understand how statistical machine learning is actually applied today. I've also created an open source project where I implemented TrueSkill three different times in increasing complexity and capability. In addition, I've created a detailed supplemental math paper that works out equations that I gloss over here. Feel free to jump to sections that look interesting and ignore ones that seem boring. Don't worry if this post seems a bit long, there are lots of pictures. It seemed easy enough: I wanted to create a database to track the skill levels of my coworkers in chess and foosball. I already knew that I wasn't very good at foosball and would bring down better players. I was curious if an algorithm could do a better job at creating well-balanced matches. I also wanted to see if I was improving at chess. I knew I needed to have an easy way to collect results from everyone and then use an algorithm that would keep getting better with more data. I was looking for a way to compress all that data and distill it down to some simple knowledge of how skilled people are. Based on some previous things that I had heard about, this seemed like a good fit for "machine learning." Machine learning is a hot area in Computer Science-- but it's intimidating. Like most subjects, there's a lot to learn to be an expert in the field. I didn't need to go very deep; I just needed to understand enough to solve my problem. I found a link to the paper describing the TrueSkill algorithm and I read it several times, but it didn't make sense. It was only 8 pages long, but it seemed beyond my capability to understand.

Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality variables. The count-min (CM) sketch is a popular approach to estimating probabilities in high-cardinality data but it does not scale well beyond a few variables. In this work, we bring together the ideas of graphical models and count sketches; and propose and analyze several approaches to estimating probabilities in structured high-cardinality streams of data. The key idea of our approximations is to use the structure of a graphical model and approximately estimate its factors by "sketches", which hash high-cardinality variables using random projections. Our approximations are computationally efficient and their space complexity is independent of the cardinality of variables. Our error bounds are multiplicative and significantly improve upon those of the CM sketch, a state-of-the-art approach to estimating probabilities in streams. We evaluate our approximations on synthetic and real-world problems, and report an order of magnitude improvements over the CM sketch.

We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between learning a 'selection function' to reveal the relevant latent variables, and use this to obtain a compact approximation of the posterior distribution for EM; this can make inference possible where the number of possible latent states is e.g. exponential in the number of latent variables, whereas an exact approach would be computationally unfeasible. We learn the selection function entirely from the observed data and current EM state via Gaussian process regression. This is by contrast with earlier approaches, where selection functions were manually-designed for each problem setting. We show that our approach performs as well as these bespoke selection functions on a wide variety of inference problems: in particular, for the challenging case of a hierarchical model for object localization with occlusion, we achieve results that match a customized state-of-the-art selection method, at a far lower computational cost.

Sum-Product Networks (SPN) have recently emerged as a new class of tractable probabilistic graphical models. Unlike Bayesian networks and Markov networks where inference may be exponential in the size of the network, inference in SPNs is in time linear in the size of the network. Since SPNs represent distributions over a fixed set of variables only, we propose dynamic sum product networks (DSPNs) as a generalization of SPNs for sequence data of varying length. A DSPN consists of a template network that is repeated as many times as needed to model data sequences of any length. We present a local search technique to learn the structure of the template network. In contrast to dynamic Bayesian networks for which inference is generally exponential in the number of variables per time slice, DSPNs inherit the linear inference complexity of SPNs. We demonstrate the advantages of DSPNs over DBNs and other models on several datasets of sequence data.