32,704 research outputs found
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.Comment: 43 page
Compressing High-Dimensional Data Spaces Using Non-Differential Augmented Vector Quantization
query processing times and space requirements. Database compression has been
discovered to alleviate the I/O bottleneck, reduce disk space, improve disk access speed,
speed up query, reduce overall retrieval time and increase the effective I/O bandwidth.
However, random access to individual tuples in a compressed database is very difficult to
achieve with most available compression techniques.
We propose a lossless compression technique called non-differential augmented vector
quantization, a close variant of the novel augmented vector quantization. The technique is
applicable to a collection of tuples and especially effective for tuples with many low to
medium cardinality fields. In addition, the technique supports standard database
operations, permits very fast random access and atomic decompression of tuples in large
collections. The technique maps a database relation into a static bitmap index cached
access structure. Consequently, we were able to achieve substantial savings in space by
storing each database tuple as a bit value in the computer memory.
Important distinguishing characteristics of our technique is that individual tuples can be
compressed and decompressed, rather than a full page or entire relation at a time, (b) the
information needed for tuple compression and decompression can reside in the memory or
at worst in a single page. Promising application domains include decision support systems,
statistical databases and life databases with low cardinality fields and possibly no text
field
Human Motion Capture Data Tailored Transform Coding
Human motion capture (mocap) is a widely used technique for digitalizing
human movements. With growing usage, compressing mocap data has received
increasing attention, since compact data size enables efficient storage and
transmission. Our analysis shows that mocap data have some unique
characteristics that distinguish themselves from images and videos. Therefore,
directly borrowing image or video compression techniques, such as discrete
cosine transform, does not work well. In this paper, we propose a novel
mocap-tailored transform coding algorithm that takes advantage of these
features. Our algorithm segments the input mocap sequences into clips, which
are represented in 2D matrices. Then it computes a set of data-dependent
orthogonal bases to transform the matrices to frequency domain, in which the
transform coefficients have significantly less dependency. Finally, the
compression is obtained by entropy coding of the quantized coefficients and the
bases. Our method has low computational cost and can be easily extended to
compress mocap databases. It also requires neither training nor complicated
parameter setting. Experimental results demonstrate that the proposed scheme
significantly outperforms state-of-the-art algorithms in terms of compression
performance and speed
Substructure Discovery Using Minimum Description Length and Background Knowledge
The ability to identify interesting and repetitive substructures is an
essential component to discovering knowledge in structural data. We describe a
new version of our SUBDUE substructure discovery system based on the minimum
description length principle. The SUBDUE system discovers substructures that
compress the original data and represent structural concepts in the data. By
replacing previously-discovered substructures in the data, multiple passes of
SUBDUE produce a hierarchical description of the structural regularities in the
data. SUBDUE uses a computationally-bounded inexact graph match that identifies
similar, but not identical, instances of a substructure and finds an
approximate measure of closeness of two substructures when under computational
constraints. In addition to the minimum description length principle, other
background knowledge can be used by SUBDUE to guide the search towards more
appropriate substructures. Experiments in a variety of domains demonstrate
SUBDUE's ability to find substructures capable of compressing the original data
and to discover structural concepts important to the domain. Description of
Online Appendix: This is a compressed tar file containing the SUBDUE discovery
system, written in C. The program accepts as input databases represented in
graph form, and will output discovered substructures with their corresponding
value.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
What Can We Learn Privately?
Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals. We demonstrate that,
ignoring computational constraints, it is possible to privately agnostically
learn any concept class using a sample size approximately logarithmic in the
cardinality of the concept class. Therefore, almost anything learnable is
learnable privately: specifically, if a concept class is learnable by a
(non-private) algorithm with polynomial sample complexity and output size, then
it can be learned privately using a polynomial number of samples. We also
present a computationally efficient private PAC learner for the class of parity
functions. Local (or randomized response) algorithms are a practical class of
private algorithms that have received extensive investigation. We provide a
precise characterization of local private learning algorithms. We show that a
concept class is learnable by a local algorithm if and only if it is learnable
in the statistical query (SQ) model. Finally, we present a separation between
the power of interactive and noninteractive local learning algorithms.Comment: 35 pages, 2 figure
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