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

The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent sets, and dominating sets. The complexity of learning vertex sets of fixed size is also investigated, and it is shown that the k-element vertex covers in a graph can be learned in a number of rounds of interaction that is independent of the size of the graph. Apart from the elegance of these algorithmic problems, the chief motivation is the surprising recently established connection between the important unsolved problem of the learning complexity of CNF (or DNF) formulas and the learning complexity of dominating sets. The complexity of teaching sets of vertices in graphs is also considered.

Algorithms for learning and teaching sets of vertices in graphs

A brief history of Edward K. Blum and the Journal of Computer and System Sciences

The authors show that the number of spanning directed trees in a regular multigraph does not depend on the selection of a reference point and on trees orientation with respect to that point. A general formula for counting the number of spanning trees in such graphs is introduced. Closed form formulae for counting spanning trees in directed and undirected Cayley graphs are given. The results obtained are applicable, for example, in the analysis of electrical networks, and in the synthesis of optimally reliable networks. In the later application the problem of finding the maximally reliable network can be replaced, under certain conditions, by the problem of finding a graph with the number of spanning trees maximized.

http://ieeexplore.ieee.org/iel3/1156/1868/00051697.pdf

Algebraic formulas for counting spanning trees in regular multigraphs

We relate NP to parameterized complexity via the ETH, SETH, and prove results on XP-optimality. Namely, we give methods to show that, under reasonable hypotheses, current algorithms for various computational tasks are optimal up to an O-factor.

The M-Hierarchy, and XP-Optimality

https://dc.tsinghuajournals.com/cgi/viewcontent.cgi?article=1512&context=tsinghua-science-and-technology

Michael R. Fellows

Papers

Algorithms for learning and teaching sets of vertices in graphs

A brief history of Edward K. Blum and the Journal of Computer and System Sciences

Algebraic formulas for counting spanning trees in regular multigraphs

The M-Hierarchy, and XP-Optimality

Some Open Problems in Parameterized Complexity Related to the Work of Jianer Chen