Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices" of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Parameterized Complexity

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

Invitation to fixed-parameter algorithms

In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.

/pdf/a-linear-time-algorithm-for-finding-tree-decompositions-of-4u8h6zpm0r.pdf

A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

In this paper we give a programmatic overview of parame-terized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how xed-parameter tractability techniques can deliver practical algorithms in two diierent ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT ker-nelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artiicial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W1]. As a corollary, this implies that k-Step Reachability for Petri Nets is complete for W1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph k-Coloring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.

Parameterized complexity: A framework for systematically confronting computational intractability.

A variety of efficient kernelization strategies for the classic vertex cover problem are developed, implemented and compared experimentally. A new technique, termed crown reduction, is introduced and analyzed. Applications to computational biology are discussed.

Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments.

Many natural computational problems have input consisting of two or more parts. For example, the input might consist of a graph and a positive integer. For many natural problems we may view one of the inputs as a parameter and study how the complexity of the problem varies if the parameter is held fixed. For many applications of computational problems involving such a parameter, only a small range of parameter values is of practical significance, so that fixed- parameter complexity is a natural concern. In studying the complexity of such problems, it is therefore important to have a framework in which we can make qualitative distinctions about the contribution of the parameter to the complexity of the problem. In this paper we survey one such framework for investigating parameterized computational complexity and present a number of new results for this theory.

Parameterized Computational Feasibility

http://www.mrfellows.net/papers/ADF95_FPTandCompletenessIV.pdf

Fixed-parameter tractability and completeness IV: On completeness for W[P] and PSPACE analogues

Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t-1)-st level W[t-1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted sat, hitting set, set cover, and feature set, cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[1] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weightedq-sat (for any fixed q>=2), clique, independent set, and dominating set, cannot be solved in time n^o^(^k^) unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n^km^O^(^1^) or O(n^k).

Michael R. Fellows

Papers

Parameterized complexity: A framework for systematically confronting computational intractability.

Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments.

Parameterized Computational Feasibility

Fixed-parameter tractability and completeness IV: On completeness for W[P] and PSPACE analogues

Tight lower bounds for certain parameterized NP-hard problems