Statistical pairwise interaction model of stock market

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.Comment: 11 pages, 8 figure

Trapped ion chain as a neural network

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit to store information distributed over the whole system. The storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential and/or by applying longitudinal local magnetic fields. The system properties suggest the possibility of implementing robust distributed realizations of quantum logic.Comment: 4 pages, 3 figure

Intrinsic limitations of inverse inference in the pairwise Ising spin glass

We analyze the limits inherent to the inverse reconstruction of a pairwise Ising spin glass based on susceptibility propagation. We establish the conditions under which the susceptibility propagation algorithm is able to reconstruct the characteristics of the network given first- and second-order local observables, evaluate eventual errors due to various types of noise in the originally observed data, and discuss the scaling of the problem with the number of degrees of freedom

Recovery Guarantees for Quadratic Tensors with Limited Observations

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models which are the sum of pairwise products instead of a triple product have emerged from applications such as recommendation systems. Non-convex methods are the method of choice for learning quadratic models, and this work examines their sample complexity and error guarantee. Our main result is that with the number of samples being only linear in the dimension, all local minima of the mean squared error objective are global minima and recover the original tensor accurately. The techniques lead to simple proofs showing that convex relaxation can recover quadratic tensors provided with linear number of samples. We substantiate our theoretical results with experiments on synthetic and real-world data, showing that quadratic models have better performance than CP models in scenarios where there are limited amount of observations available

Multi-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks

In this paper we propose the utterance-level Permutation Invariant Training (uPIT) technique. uPIT is a practically applicable, end-to-end, deep learning based solution for speaker independent multi-talker speech separation. Specifically, uPIT extends the recently proposed Permutation Invariant Training (PIT) technique with an utterance-level cost function, hence eliminating the need for solving an additional permutation problem during inference, which is otherwise required by frame-level PIT. We achieve this using Recurrent Neural Networks (RNNs) that, during training, minimize the utterance-level separation error, hence forcing separated frames belonging to the same speaker to be aligned to the same output stream. In practice, this allows RNNs, trained with uPIT, to separate multi-talker mixed speech without any prior knowledge of signal duration, number of speakers, speaker identity or gender. We evaluated uPIT on the WSJ0 and Danish two- and three-talker mixed-speech separation tasks and found that uPIT outperforms techniques based on Non-negative Matrix Factorization (NMF) and Computational Auditory Scene Analysis (CASA), and compares favorably with Deep Clustering (DPCL) and the Deep Attractor Network (DANet). Furthermore, we found that models trained with uPIT generalize well to unseen speakers and languages. Finally, we found that a single model, trained with uPIT, can handle both two-speaker, and three-speaker speech mixtures

Permutation Invariant Training of Deep Models for Speaker-Independent Multi-talker Speech Separation

We propose a novel deep learning model, which supports permutation invariant training (PIT), for speaker independent multi-talker speech separation, commonly known as the cocktail-party problem. Different from most of the prior arts that treat speech separation as a multi-class regression problem and the deep clustering technique that considers it a segmentation (or clustering) problem, our model optimizes for the separation regression error, ignoring the order of mixing sources. This strategy cleverly solves the long-lasting label permutation problem that has prevented progress on deep learning based techniques for speech separation. Experiments on the equal-energy mixing setup of a Danish corpus confirms the effectiveness of PIT. We believe improvements built upon PIT can eventually solve the cocktail-party problem and enable real-world adoption of, e.g., automatic meeting transcription and multi-party human-computer interaction, where overlapping speech is common.Comment: 5 page