[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

On robust estimation of the location parameter

KEGG(Kyoto Encyclopedia of Genes and Genomes)〔和文〕 (特集 ゲノム医学の現在と未来--基礎と臨床) -- (データベース)

Real-world relational data are seldom stationary, yet traditional collaborative filtering algorithms generally rely on this assumption. Motivated by our sales prediction problem, we propose a factor-based algorithm that is able to take time into account. By introducing additional factors for time, we formalize this problem as a tensor factorization with a special constraint on the time dimension. Further, we provide a fully Bayesian treatment to avoid tuning parameters and achieve automatic model complexity control. To learn the model we develop an efficient sampling procedure that is capable of analyzing large-scale data sets. This new algorithm, called Bayesian Probabilistic Tensor Factorization (BPTF), is evaluated on several real-world problems including sales prediction and movie recommendation. Empirical results demonstrate the superiority of our temporal model.

/pdf/temporal-collaborative-filtering-with-bayesian-probabilistic-4mc7g6w3s3.pdf

Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization

Even though many people thought the problem of finding Nash equilibria is hard in general, and it has been proven so for games among three or more players recently, it's not clear whether the two-player case can be shown in the same class of PPAD-complete problems. We prove that the problem of finding a Nash equilibrium in a two-player game is PPAD-complete

https://www.computer.org/csdl/pds/api/csdl/proceedings/download-article/12OmNzlUKm5/pdf

Settling the Complexity of Two-Player Nash Equilibrium

We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991.Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing open problem in algorithmic game theory. It also serves as a starting point for a series of results concerning the complexity of two-player Nash equilibria. In particular, we prove the following theorems:—Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time.—The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time.Our results also have a complexity implication in mathematical economics:—Arrow-Debreu market equilibria are PPAD-hard to compute.

Settling the complexity of computing two-player Nash equilibria

We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. 
This is the first of a series of results concerning the complexity of Nash equilibria. In particular, we prove the following theorems: 
Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results demonstrate that, even in the simplest form of non-cooperative games, equilibrium computation and approximation are polynomial-time equivalent to fixed point computation. Our results also have two broad complexity implications in mathematical economics and operations research: Arrow-Debreu market equilibria are PPAD-hard to compute. The P-Matrix Linear Complementary Problem is computationally harder than convex programming unless every problem in PPAD is solvable in polynomial time.

Settling the Complexity of Computing Two-Player Nash Equilibria

Inferring rankings over elements of a set of objects, such as documents or images, is a key learning problem for such important applications as Web search and recommender systems. Crowdsourcing services provide an inexpensive and efficient means to acquire preferences over objects via labeling by sets of annotators. We propose a new model to predict a gold-standard ranking that hinges on combining pairwise comparisons via crowdsourcing. In contrast to traditional ranking aggregation methods, the approach learns about and folds into consideration the quality of contributions of each annotator. In addition, we minimize the cost of assessment by introducing a generalization of the traditional active learning scenario to jointly select the annotator and pair to assess while taking into account the annotator quality, the uncertainty over ordering of the pair, and the current model uncertainty. We formalize this as an active learning strategy that incorporates an exploration-exploitation tradeoff and implement it using an efficient online Bayesian updating scheme. Using simulated and real-world data, we demonstrate that the active learning strategy achieves significant reductions in labeling cost while maintaining accuracy.

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Xi Chen

Papers

Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization

Settling the Complexity of Two-Player Nash Equilibrium

Settling the complexity of computing two-player Nash equilibria

Settling the Complexity of Computing Two-Player Nash Equilibria

Pairwise ranking aggregation in a crowdsourced setting