The Attitude Toward Probabilities of Portfolio Managers : an Experimental Study

This paper proposes an experiment about the attitude toward probabilities on a population of portfolio managers. Its aim is to check whether or not portfolio managers are neutral toward probabilities. Meanwhile, it presents a experimental protocole that highlights an inconsistency between two experimental techniques. It also introduces a new functional form for the probability weighting function. Results unambiguously show that portfolio managers are not neutral toward probabilities and that they display a strong heterogeneity in their preferences.Attitude toward probabilities, probability weighting function, expected utility, rank dependent expected utility, experimental economics, decision under risk.

Local Component Analysis

Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier work has focused on learning only the bandwidth of the kernel (i.e., a scalar multiplicative factor). In this paper, we propose to learn a full Euclidean metric through an expectation-minimization (EM) procedure, which can be seen as an unsupervised counterpart to neighbourhood component analysis (NCA). In order to avoid overfitting with a fully nonparametric density estimator in high dimensions, we also consider a semi-parametric Gaussian-Parzen density model, where some of the variables are modelled through a jointly Gaussian density, while others are modelled through Parzen windows. For these two models, EM leads to simple closed-form updates based on matrix inversions and eigenvalue decompositions. We show empirically that our method leads to density estimators with higher test-likelihoods than natural competing methods, and that the metrics may be used within most unsupervised learning techniques that rely on such metrics, such as spectral clustering or manifold learning methods. Finally, we present a stochastic approximation scheme which allows for the use of this method in a large-scale setting

Knowledge flows and the geography of networks. A strategic model of small worlds formation.

This paper aims to demonstrate that the strategic approach of network formation can generate networks that share the main structural properties of most real social networks. We introduce a spatialized variation of the Connections model (Jackson and Wolinski, 1996) in which agents balance the benefits of forming links resulting from imperfect knowledge flows through bonds against their costs which increase with geographic distance. We show that, for intermediary levels of knowledge transferability, our time-inhomogeneous process selects networks which exhibit high clustering, short average distances and, when the costs of link formation are normally distributed across agents, skewed degree distributions.Strategic network formation ; Time-inhomogeneous process ; Knowledge flows ; Small worlds ; Monte Carlo simulations.

A strategic model of complex networks formation.

This paper introduces a spatialized variation of the Connections model of Jackson and Wolinski (1996). Agents benefit from their direct and indirect connections in a communication network. They are arranged on a circle and bear costs for maintaining direct connections which are linearly increasing with geographic distance. In a dynamic setting, this model is shown to generate networks that exhibit the small world properties shared by many real social and economic networks.Strategic Network Formation, Pairwise Stability, Small World, Monte Carlo.

Magnetic responses of randomly depleted spin ladders

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.Comment: 24 pages, 20 figure

Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.Comment: 13 pages, 13 figure

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.Comment: Neural Information Processing Systems (2011

Minimizing Finite Sums with the Stochastic Average Gradient

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from O(1/k^{1/2}) to O(1/k) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear O(1/k) to a linear convergence rate of the form O(p^k) for p \textless{} 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.Comment: Revision from January 2015 submission. Major changes: updated literature follow and discussion of subsequent work, additional Lemma showing the validity of one of the formulas, somewhat simplified presentation of Lyapunov bound, included code needed for checking proofs rather than the polynomials generated by the code, added error regions to the numerical experiment