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Bart De Moor

Publications and source records attributed to Bart De Moor.

At least 37 records · Page 2Linked to original sources

A Robust Ensemble Approach to Learn From Positive and Unlabeled Data Using SVM Base Models

We present a novel approach to learn binary classifiers when only positive and unlabeled instances are available (PU learning). This problem is routinely cast as a supervised task with label noise in the negative set. We use an ensemble of SVM models trained on bootstrap resamples of the training data for increased robustness against label noise. The approach can be considered in a bagging framework which provides an intuitive explanation for its mechanics in a semi-supervised setting. We compared our method to state-of-the-art approaches in simulations using multiple public benchmark data sets. The included benchmark comprises three settings with increasing label noise: (i) fully supervised, (ii) PU learning and (iii) PU learning with false positives. Our approach shows a marginal improvement over existing methods in the second setting and a significant improvement in the third.

stat.ML↗

Fast Prediction with SVM Models Containing RBF Kernels

We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The approximation is applicable to all kernel methods featuring sums of kernel evaluations and makes no assumptions regarding data normalization. The prediction speed of approximated models no longer relates to the amount of support vectors but is quadratic in terms of the number of input dimensions. If the number of input dimensions is small compared to the amount of support vectors, the approximated model is significantly faster in prediction and has a smaller memory footprint. An optimized C++ implementation was made to assess the gain in prediction speed in a set of practical tests. We additionally provide a method to verify the approximation accuracy, prior to training models or during run-time, to ensure the loss in accuracy remains acceptable and within known bounds.

stat.ML↗

EnsembleSVM: A Library for Ensemble Learning Using Support Vector Machines

EnsembleSVM is a free software package containing efficient routines to perform ensemble learning with support vector machine (SVM) base models. It currently offers ensemble methods based on binary SVM models. Our implementation avoids duplicate storage and evaluation of support vectors which are shared between constituent models. Experimental results show that using ensemble approaches can drastically reduce training complexity while maintaining high predictive accuracy. The EnsembleSVM software package is freely available online at http://esat.kuleuven.be/stadius/ensemblesvm.

stat.ML↗

Geometric Analogue of Holographic Reduced Representation

Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Variable bindings occurring in both HRR and its geometric analogue mathematically correspond to two different representations of $Z_2\times...\times Z_2$ (the additive group of binary $n$-tuples with addition modulo 2). As opposed to standard HRR, variable binding performed by means of geometric product allows for computing exact inverses of all nonzero vectors, a procedure even simpler than approximate inverses employed in HRR. The formal structure of the new reduced representation is analogous to cartoon computation, a geometric analogue of quantum computation.

cs.AI↗

Support and Quantile Tubes

This correspondence studies an estimator of the conditional support of a distribution underlying a set of i.i.d. observations. The relation with mutual information is shown via an extension of Fano's theorem in combination with a generalization bound based on a compression argument. Extensions to estimating the conditional quantile interval, and statistical guarantees on the minimal convex hull are given.

cs.IT↗

Stabilizer state breeding

We present a breeding protocol that distills pure copies of any stabilizer state from noisy copies and a pool of predistilled pure copies of the same state, by means of local Clifford operations, Pauli measurements and classical communication.

quant-ph↗

Asymptotic adaptive bipartite entanglement distillation protocol

We present a new asymptotic bipartite entanglement distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace measurements on ebits by measurements on a finite number of copies, whenever there are two equiprobable outcomes. In that case, the entropy of the global state is reduced by more than one bit. Therefore, every such replacement results in an improvement of the protocol. We explain how our protocol is organized as to have as many replacements as possible. The yield is then calculated for Werner states.

quant-ph↗

Hashing protocol for distilling multipartite CSS states

We present a hashing protocol for distilling multipartite CSS states by means of local Clifford operations, Pauli measurements and classical communication. It is shown that this hashing protocol outperforms previous versions by exploiting information theory to a full extent an not only applying CNOTs as local Clifford operations. Using the information-theoretical notion of a strongly typical set, we calculate the asymptotic yield of the protocol as the solution of a linear programming problem.

quant-ph↗

Edge-local equivalence of graphs

The local complement G*i of a simple graph G at one of its vertices i is obtained by complementing the subgraph induced by the neighborhood of i and leaving the rest of the graph unchanged. If e={i,j} is an edge of G then G*e=((G*i)*j)*i is called the edge-local complement of G along the edge e. We call two graphs edge-locally equivalent if they are related by a sequence of edge-local complementations. The main result of this paper is an algebraic description of edge-local equivalence of graphs in terms of linear fractional transformations of adjacency matrices. Applications of this result include (i) a polynomial algorithm to recognize whether two graphs are edge-locally equivalent, (ii) a formula to count the number of graphs in a class of edge-local equivalence, and (iii) a result concerning the coefficients of the interlace polynomial, where we show that these coefficients are all even for a class of graphs; this class contains, as a subset, all strongly regular graphs with parameters (n, k, a, c), where k is odd and a and c are even.

math.CO↗

Cellular Automata Models of Road Traffic

In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of statistical mechanics, having the goal of reproducing the correct macroscopic behaviour based on a minimal description of microscopic interactions. After giving an overview of cellular automata (CA) models, their background and physical setup, we introduce the mathematical notations, show how to perform measurements on a TCA model's lattice of cells, as well as how to convert these quantities into real-world units and vice versa. The majority of this paper then relays an extensive account of the behavioural aspects of several TCA models encountered in literature. Already, several reviews of TCA models exist, but none of them consider all the models exclusively from the behavioural point of view. In this respect, our overview fills this void, as it focusses on the behaviour of the TCA models, by means of time-space and phase-space diagrams, and histograms showing the distributions of vehicles' speeds, space, and time gaps. In the report, we subsequently give a concise overview of TCA models that are employed in a multi-lane setting, and some of the TCA models used to describe city traffic as a two-dimensional grid of cells, or as a road network with explicitly modelled intersections. The final part of the paper illustrates some of the more common analytical approximations to single-cell TCA models.

physics.soc-ph↗

Traffic Flow Theory

The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with respect to traffic flow theory. Starting with a brief history, we introduce the microscopic and macroscopic characteristics of vehicular traffic flows. Moving on, we review some performance indicators that allow us to assess the quality of traffic operations. A final part of this paper discusses some of the relations between traffic flow characteristics, i.e., the fundamental diagrams, and sheds some light on the different points of view adopted by the traffic engineering community.

physics.soc-ph↗

Transportation Planning and Traffic Flow Models

In this paper, we focus on the different traffic flow models that exist in literature. Due to our frequently encountered confusion among traffic engineers and policy makers, this paper goes into more detail about transportation planning models on the one hand, and traffic flow models on the other hand. The former deal with households that make certain decisions which lead to transportation and the use of infrastructure, as opposed to the latter which explicitly describe the physical propagation of traffic flows in a road network. Our goal is not to give a full account (as that would be a dissertation of its own, given the broadness of the field), but rather to impose upon the reader a thorough feeling for the differences between transportation planning and traffic flow models. Because of the high course of progress over the last decade (or even during the last five years), this paper tries to chronicle both past models, as well as some of the latest developments in this area.

physics.soc-ph↗

Relating the dynamics of road traffic in a stochastic cellular automaton to a macroscopic first-order model

In this paper, we describe a relation between a microscopic traffic cellular automaton (TCA) model (i.e., the stochastic TCA model of Nagel and Schreckenberg) and the macroscopic first-order hydrodynamic model of Lighthill, Whitham, and Richards (LWR). The innovative aspect of our approach, is that we explicitly derive the LWR's fundamental diagram directly from the STCA's rule set, by assuming a stationarity condition that converts the STCA's rules into a set of linear inequalities. In turn, these constraints define the shape of the fundamental diagram, which is then specified to the LWR model. Application of our methodology to a simulation case study, allows us to compare the tempo-spatial behavior of both models. Our results indicate that, in the presence of noise, the capacity flows in the derived fundamental diagram are overestimations of those of the STCA model. Directly specifying the STCA's capacity flows to the LWR fundamental diagram, effectively remedies most of the mismatches between both approaches. Our methodology sees the STCA complementary to the LWR model and vice versa, so the results can be of great assistance when interpreting the traffic dynamics in both models. Especially appealing, is the fact that the STCA can visualize the higher-order characteristics of traffic stream dynamics, e.g., the fans of rarefaction waves.

physics.soc-ph↗

Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton

Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium.

cond-mat.stat-mech↗

Componentwise Least Squares Support Vector Machines

This chapter describes componentwise Least Squares Support Vector Machines (LS-SVMs) for the estimation of additive models consisting of a sum of nonlinear components. The primal-dual derivations characterizing LS-SVMs for the estimation of the additive model result in a single set of linear equations with size growing in the number of data-points. The derivation is elaborated for the classification as well as the regression case. Furthermore, different techniques are proposed to discover structure in the data by looking for sparse components in the model based on dedicated regularization schemes on the one hand and fusion of the componentwise LS-SVMs training with a validation criterion on the other hand. (keywords: LS-SVMs, additive models, regularization, structure detection)

cs.LG↗

Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic

We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over the integers modulo d. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.

quant-ph↗

The invariants of the local Clifford group

We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Clifford operators in terms of linear operations over GF(2). Such a study of polynomial invariants of the local Clifford group is mainly of importance in quantum coding theory, in particular in the classification of binary quantum codes. Some applications in entanglement theory and quantum computing are briefly discussed as well.

quant-ph↗