317,879 research outputs found
Learning over Knowledge-Base Embeddings for Recommendation
State-of-the-art recommendation algorithms -- especially the collaborative
filtering (CF) based approaches with shallow or deep models -- usually work
with various unstructured information sources for recommendation, such as
textual reviews, visual images, and various implicit or explicit feedbacks.
Though structured knowledge bases were considered in content-based approaches,
they have been largely neglected recently due to the availability of vast
amount of data, and the learning power of many complex models.
However, structured knowledge bases exhibit unique advantages in personalized
recommendation systems. When the explicit knowledge about users and items is
considered for recommendation, the system could provide highly customized
recommendations based on users' historical behaviors. A great challenge for
using knowledge bases for recommendation is how to integrated large-scale
structured and unstructured data, while taking advantage of collaborative
filtering for highly accurate performance. Recent achievements on knowledge
base embedding sheds light on this problem, which makes it possible to learn
user and item representations while preserving the structure of their
relationship with external knowledge. In this work, we propose to reason over
knowledge base embeddings for personalized recommendation. Specifically, we
propose a knowledge base representation learning approach to embed
heterogeneous entities for recommendation. Experimental results on real-world
dataset verified the superior performance of our approach compared with
state-of-the-art baselines
Combining open and closed world reasoning for the semantic web
Dissertação para obtenção do Grau de Doutor
em InformáticaOne important problem in the ongoing standardization of knowledge representation
languages for the Semantic Web is combining open world ontology languages, such as the OWL-based ones, and closed world rule-based languages.
The main difficulty of such a combination is that both formalisms are quite orthogonal w.r.t. expressiveness and how decidability is achieved. Combining non-monotonic rules and ontologies is thus a challenging task
that requires careful balancing between expressiveness of the knowledge representation language and the computational complexity of reasoning.
In this thesis, we will argue in favor of a combination of ontologies and nonmonotonic
rules that tightly integrates the two formalisms involved, that has a computational complexity that is as low as possible, and that allows us to query for information instead of calculating the whole model. As our starting point we choose the mature approach of hybrid MKNF knowledge
bases, which is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. We extend the two-valued framework of MKNF logics to a three-valued logics, and we propose a well-founded semantics for non-disjunctive hybrid MKNF knowledge bases. This new semantics promises to provide better efficiency of reasoning,and it is faithful w.r.t. the original two-valued MKNF semantics and compatible with both the OWL-based semantics and the traditional Well-
Founded Semantics for logic programs. We provide an algorithm based on operators to compute the unique model, and we extend SLG resolution with tabling to a general framework that allows us to query a combination of non-monotonic rules and any given ontology language. Finally, we
investigate concrete instances of that procedure w.r.t. three tractable ontology
languages, namely the three description logics underlying the OWL 2 pro les.Fundação para a Ciência e Tecnologia - grant contract SFRH/BD/28745/200
Uncertainty Relations for Shift-Invariant Analog Signals
The past several years have witnessed a surge of research investigating
various aspects of sparse representations and compressed sensing. Most of this
work has focused on the finite-dimensional setting in which the goal is to
decompose a finite-length vector into a given finite dictionary. Underlying
many of these results is the conceptual notion of an uncertainty principle: a
signal cannot be sparsely represented in two different bases. Here, we extend
these ideas and results to the analog, infinite-dimensional setting by
considering signals that lie in a finitely-generated shift-invariant (SI)
space. This class of signals is rich enough to include many interesting special
cases such as multiband signals and splines. By adapting the notion of
coherence defined for finite dictionaries to infinite SI representations, we
develop an uncertainty principle similar in spirit to its finite counterpart.
We demonstrate tightness of our bound by considering a bandlimited lowpass
train that achieves the uncertainty principle. Building upon these results and
similar work in the finite setting, we show how to find a sparse decomposition
in an overcomplete dictionary by solving a convex optimization problem. The
distinguishing feature of our approach is the fact that even though the problem
is defined over an infinite domain with infinitely many variables and
constraints, under certain conditions on the dictionary spectrum our algorithm
can find the sparsest representation by solving a finite-dimensional problem.Comment: Accepted to IEEE Trans. on Inform. Theor
On implicational bases of closure systems with unique critical sets
We show that every optimum basis of a finite closure system, in D.Maier's
sense, is also right-side optimum, which is a parameter of a minimum CNF
representation of a Horn Boolean function. New parameters for the size of the
binary part are also established. We introduce a K-basis of a general closure
system, which is a refinement of the canonical basis of Duquenne and Guigues,
and discuss a polynomial algorithm to obtain it. We study closure systems with
the unique criticals and some of its subclasses, where the K-basis is unique. A
further refinement in the form of the E-basis is possible for closure systems
without D-cycles. There is a polynomial algorithm to recognize the D-relation
from a K-basis. Thus, closure systems without D-cycles can be effectively
recognized. While E-basis achieves an optimum in one of its parts, the
optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and
Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into
plenary talk on conference Universal Algebra and Lattice Theory, June 2012,
Szeged, Hungary 29 pages and 2 figure
On Sparse Representation in Fourier and Local Bases
We consider the classical problem of finding the sparse representation of a
signal in a pair of bases. When both bases are orthogonal, it is known that the
sparse representation is unique when the sparsity of the signal satisfies
, where is the mutual coherence of the dictionary.
Furthermore, the sparse representation can be obtained in polynomial time by
Basis Pursuit (BP), when . Therefore, there is a gap between the
unicity condition and the one required to use the polynomial-complexity BP
formulation. For the case of general dictionaries, it is also well known that
finding the sparse representation under the only constraint of unicity is
NP-hard.
In this paper, we introduce, for the case of Fourier and canonical bases, a
polynomial complexity algorithm that finds all the possible -sparse
representations of a signal under the weaker condition that . Consequently, when , the proposed algorithm solves the
unique sparse representation problem for this structured dictionary in
polynomial time. We further show that the same method can be extended to many
other pairs of bases, one of which must have local atoms. Examples include the
union of Fourier and local Fourier bases, the union of discrete cosine
transform and canonical bases, and the union of random Gaussian and canonical
bases
Greed is good: algorithmic results for sparse approximation
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho's basis pursuit (BP) paradigm can recover the optimal representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function is introduced to quantify the level of incoherence. This analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal. From there, it argues that OMP is an approximation algorithm for the sparse problem over a quasi-incoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms
The inverse problem for representation functions for general linear forms
The inverse problem for representation functions takes as input a triple
(X,f,L), where X is a countable semigroup, f : X --> N_0 \cup {\infty} a
function, L : a_1 x_1 + ... + a_h x_h an X-linear form and asks for a subset A
\subseteq X such that there are f(x) solutions (counted appropriately) to
L(x_1,...,x_h) = x for every x \in X, or a proof that no such subset exists.
This paper represents the first systematic study of this problem for
arbitrary linear forms when X = Z, the setting which in many respects is the
most natural one. Having first settled on the "right" way to count
representations, we prove that every primitive form has a unique representation
basis, i.e.: a set A which represents the function f \equiv 1. We also prove
that a partition regular form (i.e.: one for which no non-empty subset of the
coefficients sums to zero) represents any function f for which {f^{-1}(0)} has
zero asymptotic density. These two results answer questions recently posed by
Nathanson.
The inverse problem for partition irregular forms seems to be more
complicated. The simplest example of such a form is x_1 - x_2, and for this
form we provide some partial results. Several remaining open problems are
discussed.Comment: 15 pages, no figure
Covariant mutually unbiased bases
The connection between maximal sets of mutually unbiased bases (MUBs) in a
prime-power dimensional Hilbert space and finite phase-space geometries is well
known. In this article we classify MUBs according to their degree of covariance
with respect to the natural symmetries of a finite phase-space, which are the
group of its affine symplectic transformations. We prove that there exist
maximal sets of MUBs that are covariant with respect to the full group only in
odd prime-power dimensional spaces, and in this case their equivalence class is
actually unique. Despite this limitation, we show that in even-prime power
dimension covariance can still be achieved by restricting to proper subgroups
of the symplectic group, that constitute the finite analogues of the oscillator
group. For these subgroups, we explicitly construct the unitary operators
yielding the covariance.Comment: 44 pages, some remarks and references added in v
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