Given a computable probability measure P over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of P.
Information conservation laws were introduced and studied in @cite_15 @cite_8 . Information asymmetry and the complexity of complexity were studied in @cite_0 . A history of the origin of the mutual information of a string with the halting sequence can be found in @cite_23 .
@cite_0 @cite_15 @cite_23 @cite_8
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The paper presents interpretations of some recently discovered laws of evolution and conservation in the largeprogram life cycle. Program development and maintenance processes are managed and implemented by people; thus in the long term they could be expected to be unpredictable, dependant on the judgments, whims, and actions of programming process participants (e.g., managers, programmers, and product users). Yet, observed, measured, and modeled regularities suggest laws that are closer to biological laws or those of modern physics than to those currently formulated in other areas subject to human influence (e.g., economics and sociology). After a brief discussion of the first four laws, to highlight underlying phenomena and natural attributes of the program evolution process, the paper concentrates on a fifth law and shows how, and why, this law represents a conservation phenomenon: the Conservation of Familiarity. In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by [Lecture Notes in Comput. Sci. 3876, Springer, New York, 2006, pp. 265--284] that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private probably approximately correct (PAC) and agnostic learning was studied in a number of prior works starting with [SIAM J. Comput., 40 (2011), pp. 793--826]. However, a number of basic questions remain open [A. Beimel, S. P. Kasiviswanathan, and K. Nissim, Lecture Notes in Comput. Sci. 5978, Springer, New York, 2006, pp. 437--454; K. Chaudhuri and D. Hsu, Proceedings of Conference in Learning Theory, 2011, pp. 155--186; A. Beimel, K. Nissim, and U. Stemmer, Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, 2013, pp. 9... We describe a legal question answering system which combines legal information retrieval and textual entailment. We have evaluated our system using the data from the first competition on legal information extraction entailment (COLIEE) 2014. The competition focuses on two aspects of legal information processing related to answering yes no questions from Japanese legal bar exams. The shared task consists of two phases: legal ad hoc information retrieval and textual entailment. The first phase requires the identification of Japan civil law articles relevant to a legal bar exam query. We have implemented two unsupervised baseline models (tf-idf and Latent Dirichlet Allocation (LDA)-based Information Retrieval (IR)), and a supervised model, Ranking SVM, for the task. The features of the model are a set of words, and scores of an article based on the corresponding baseline models. The results show that the Ranking SVM model nearly doubles the Mean Average Precision compared with both baseline models. The second phase is to answer “Yes” or “No” to previously unseen queries, by comparing the meanings of queries with relevant articles. The features used for phase two are syntactic semantic similarities and identification of negation antonym relations. The results show that our method, combined with rule-based model and the unsupervised model, outperforms the SVM-based supervised model. Consider a linear [n,k,d]q code C. We say that the ith coordinate of C has locality r , if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small redundancy, low locality for information coordinates, large distance, and low locality for parity coordinates. In this paper, we carry out an in-depth study of the relations between these parameters. We establish a tight bound for the redundancy n-k in terms of the message length, the distance, and the locality of information coordinates. We refer to codes attaining the bound as optimal. We prove some structure theorems about optimal codes, which are particularly strong for small distances. This gives a fairly complete picture of the tradeoffs between codewords length, worst case distance, and locality of information symbols. We then consider the locality of parity check symbols and erasure correction beyond worst case distance for optimal codes. Using our structure theorem, we obtain a tight bound for the locality of parity symbols possible in such codes for a broad class of parameter settings. We prove that there is a tradeoff between having good locality and the ability to correct erasures beyond the minimum distance.