28,539 research outputs found
Dual-to-kernel learning with ideals
In this paper, we propose a theory which unifies kernel learning and symbolic
algebraic methods. We show that both worlds are inherently dual to each other,
and we use this duality to combine the structure-awareness of algebraic methods
with the efficiency and generality of kernels. The main idea lies in relating
polynomial rings to feature space, and ideals to manifolds, then exploiting
this generative-discriminative duality on kernel matrices. We illustrate this
by proposing two algorithms, IPCA and AVICA, for simultaneous manifold and
feature learning, and test their accuracy on synthetic and real world data.Comment: 15 pages, 1 figur
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
Credible Autocoding of Convex Optimization Algorithms
The efficiency of modern optimization methods, coupled with increasing
computational resources, has led to the possibility of real-time optimization
algorithms acting in safety critical roles. There is a considerable body of
mathematical proofs on on-line optimization programs which can be leveraged to
assist in the development and verification of their implementation. In this
paper, we demonstrate how theoretical proofs of real-time optimization
algorithms can be used to describe functional properties at the level of the
code, thereby making it accessible for the formal methods community. The
running example used in this paper is a generic semi-definite programming (SDP)
solver. Semi-definite programs can encode a wide variety of optimization
problems and can be solved in polynomial time at a given accuracy. We describe
a top-to-down approach that transforms a high-level analysis of the algorithm
into useful code annotations. We formulate some general remarks about how such
a task can be incorporated into a convex programming autocoder. We then take a
first step towards the automatic verification of the optimization program by
identifying key issues to be adressed in future work
An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems
We develop an inexact primal-dual first-order smoothing framework to solve a
class of non-bilinear saddle point problems with primal strong convexity.
Compared with existing methods, our framework yields a significant improvement
over the primal oracle complexity, while it has competitive dual oracle
complexity. In addition, we consider the situation where the primal-dual
coupling term has a large number of component functions. To efficiently handle
this situation, we develop a randomized version of our smoothing framework,
which allows the primal and dual sub-problems in each iteration to be solved by
randomized algorithms inexactly in expectation. The convergence of this
framework is analyzed both in expectation and with high probability. In terms
of the primal and dual oracle complexities, this framework significantly
improves over its deterministic counterpart. As an important application, we
adapt both frameworks for solving convex optimization problems with many
functional constraints. To obtain an -optimal and
-feasible solution, both frameworks achieve the best-known oracle
complexities (in terms of their dependence on )
BROJA-2PID: A robust estimator for bivariate partial information decomposition
Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the
most robust to compute the Bertschinger et al. partial information decompostion
(BROJA PID) measure [1]. We developed a production-quality robust software that
computes the BROJA PID measure based on the Cone Programming model. In this
paper, we prove the important property of strong duality for the Cone Program
and prove an equivalence between the Cone Program and the original Convex
problem. Then describe in detail our software and how to use it.\newline\inden
Advances in QCD sum rule calculations
We review the recent progress in the applications of QCD sum rules to hadron
properties with the emphasis on the following selected problems: (i)
development of new algorithms for the extraction of ground-state parameters
from two-point correlators; (ii) form factors at large momentum transfers from
three-point vacuum correlation functions; (iii) properties of exotic tetraquark
hadrons from correlation functions of four-quark currents.Comment: 12 pages, plenary talk given at the XIth International Conference on
Quark Confinement and the Hadron Spectrum, Saint Petersburg, Russia,
September 8-12, 201
- …