1,720,974 research outputs found
Legendre equivalences of spherical Boltzmann machines
Full text linkWe study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove that the free energies of the spherical and Gaussian models are related by a Legendre transformation. Incidentally our analysis brings also a new purely variational derivation of the free energy of the spherical models
Unveiling the relation between herding and liquidity with trader lead-lag networks
Full text linkWe propose a method to infer lead-lag networks of traders from the observation of their trade record as well as to reconstruct their state of supply and demand when they do not trade. The method relies on the Kinetic Ising model to describe how information propagates among traders, assigning a positive or negative ‘opinion’ to all agents about whether the traded asset price will go up or down. This opinion is reflected by their trading behavior, but whenever the trader is not active in a given time window, a missing value will arise. Using a recently developed inference algorithm, we are able to reconstruct a lead-lag network and to estimate the unobserved opinions, giving a clearer picture about the state of supply and demand in the market at all times. We apply our method to a dataset of clients of a major dealer in the Foreign Exchange market at the 5 minute time scale. We identify leading players in the market and define a herding measure based on the observed and inferred opinions. We show the causal link between herding and liquidity in the inter-dealer market used by dealers to rebalance their inventories
Disentangling group and link persistence in dynamic stochastic block models
Full text linkWe study the inference of a model of dynamic networks in which both communities and links keep memory of previous network states. By considering maximum likelihood inference from single snapshot observations of the network, we show that link persistence makes the inference of communities harder, decreasing the detectability threshold, while community persistence tends to make it easier. We analytically show that communities inferred from single network snapshot can share a maximum overlap with the underlying communities of a specific previous instant in time. This leads to time-lagged inference: the identification of past communities rather than present ones. Finally we compute the time lag and propose a corrected algorithm, the lagged snapshot dynamic algorithm, for community detection in dynamic networks. We analytically and numerically characterize the detectability transitions of such algorithm as a function of the memory parameters of the model and we make a comparison with a full dynamic inference
A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market
Full text linkWe propose a dynamic network model where two mechanisms control the probability of a link between two nodes: (i) the existence or absence of this link in the past, and (ii) node-specific latent variables (dynamic fitnesses) describing the propensity of each node to create links. Assuming a Markov dynamics for both mechanisms, we propose an Expectation-Maximization algorithm for model estimation and inference of the latent variables. The estimated parameters and fitnesses can be used to forecast the presence of a link in the future. We apply our methodology to the e-MID interbank network for which the two linkage mechanisms are associated with two different trading behaviors in the process of network formation, namely preferential trading and trading driven by node-specific characteristics. The empirical results allow to recognize preferential lending in the interbank market and indicate how a method that does not account for time-varying network topologies tends to overestimate preferential linkage
Inference of the kinetic Ising model with heterogeneous missing data
Full text linkWe consider the problem of inferring a causality structure from multiple binary time series by using the kinetic Ising model in datasets where a fraction of observations is missing. Inspired by recent work on mean field methods for the inference of the model with hidden spins, we develop a pseudo-expectation-maximization algorithm that is able to work even in conditions of severe data sparsity. The methodology relies on the Martin-Siggia-Rose path integral method with second-order saddle-point solution to make it possible to approximate the log-likelihood in polynomial time, giving as output an estimate of the couplings matrix and of the missing observations. We also propose a recursive version of the algorithm, where at every iteration some missing values are substituted by their maximum-likelihood estimate, showing that the method can be used together with sparsification schemes such as lasso regularization or decimation. We test the performance of the algorithm on synthetic data and find interesting properties regarding the dependency on heterogeneity of the observation frequency of spins and when some of the hypotheses that are necessary to the saddle-point approximation are violated, such as the small couplings limit and the assumption of statistical independence between couplings
Deep Reinforcement Trading with Predictable Returns
Full text linkClassical portfolio optimization often requires forecasting asset returns and
their corresponding variances in spite of the low signal-to-noise ratio
provided in the financial markets. Modern deep reinforcement learning (DRL)
offers a framework for optimizing sequential trader decisions but lacks
theoretical guarantees of convergence. On the other hand, the performances on
real financial trading problems are strongly affected by the goodness of the
signal used to predict returns. To disentangle the effects coming from return
unpredictability from those coming from algorithm un-trainability, we
investigate the performance of model-free DRL traders in a market environment
with different known mean-reverting factors driving the dynamics. When the
framework admits an exact dynamic programming solution, we can assess the
limits and capabilities of different value-based algorithms to retrieve
meaningful trading signals in a data-driven manner. We consider DRL agents that
leverage classical strategies to increase their performances and we show that
this approach guarantees flexibility, outperforming the benchmark strategy when
the price dynamics is misspecified and some original assumptions on the market
environment are violated with the presence of extreme events and volatility
clustering.Comment: 37 pages, 15 figures. Added a more detailed appendix explaining the
approached followed. Revised version to be published in Physyca
Inverse problems for structured datasets using parallel TAP equations and restricted Boltzmann machines
Full text linkWe propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This problem has been widely analyzed through various methods such as mean-field approaches or the pseudo-likelihood optimization. Our approach is based on the estimation of the posterior using the Thouless–Anderson–Palmer (TAP) equations in a parallel updating scheme. Unlike other methods, it allows to retrieve the original patterns of the teacher dataset and thanks to the parallel update it can be applied to large system sizes. We tackle the same problem using a restricted Boltzmann machine (RBM) and discuss analogies and differences between our algorithm and RBM learning
Dense Hopfield networks in the teacher-student setting
Full text linkDense Hopfield networks with p-body interactions are known for their feature to prototype transition and adversarial robustness. However, theoretical studies have been mostly concerned with their storage capacity. We derive the phase diagram of pattern retrieval in the teacher-student setting of p-body networks, finding ferromagnetic phases reminiscent of the prototype and feature learning regimes. On the Nishimori line, we find the critical amount of data necessary for pattern retrieval, and we show that the corresponding ferromagnetic transition coincides with the paramagnetic to spin-glass transition of p-body networks with random memories. Outside of the Nishimori line, we find that the student can tolerate extensive noise when it has a larger p than the teacher. We derive a formula for the adversarial robustness of such a student at zero temperature, corroborating the positive correlation between number of parameters and robustness in large neural networks. Our model also clarifies why the prototype phase of p-body networks is adversarially robust
Reinforcement Learning Policy Recommendation for Interbank Network Stability
Full text linkIn this paper, we analyze the effect of a policy recommendation on the
performance of an artificial interbank market. Financial institutions stipulate
lending agreements following a public recommendation and their individual
information. The former is modeled by a reinforcement learning optimal policy
that maximizes the system's fitness and gathers information on the economic
environment. The policy recommendation directs economic actors to create credit
relationships through the optimal choice between a low interest rate or a high
liquidity supply. The latter, based on the agents' balance sheet, allows
determining the liquidity supply and interest rate that the banks optimally
offer their clients within the market. Thanks to the combination between the
public and the private signal, financial institutions create or cut their
credit connections over time via a preferential attachment evolving procedure
able to generate a dynamic network. Our results show that the emergence of a
core-periphery interbank network, combined with a certain level of homogeneity
in the size of lenders and borrowers, is essential to ensure the system's
resilience. Moreover, the optimal policy recommendation obtained through
reinforcement learning is crucial in mitigating systemic risk.Comment: 63 pages, 24 figures. Submitted the revised version that is going to
be published on the Journal of Financial Stabilit
Assessing the role of migration as trade-facilitator using the statistical mechanics of cooperative systems
Full text linkInteractions between natives and foreign-born individuals may help to stimulate the development and the diversification of bilateral trade relationships. In fact, migrants act as trade facilitators reducing transaction costs in export activities and, consequently, more local firms are able to establish new trade relationships abroad. The pro-trade effect of migration is well evidenced in several works where the shape of the trade-migration relationship has been examined empirically; however, they all lack an analytical model that enables them to predict the expected non-linear relationship between migration and trade. Here, using statistical mechanics tools we develop a simple model that demonstrates that there is a positive non-linear relationship between the extensive margin of trade and the proportion of migrants in the total population. Data on Spanish trade and migration provide support for the predictions made by the theoretical model. The model also suggests the need of a critical mass of migrants before their interactions with the natives have any effective impact on trade. The threshold is sensitive to the nationality of the migrants, suggesting that cultural differences between natives and migrants may affect the number of migrants needed to generate a positive impact on trade. Furthermore, we examine the possible relationship between the share of migrants in the total population and the extent of diversification of the portfolio of exported goods, finding evidence of a strong positive correlation. Our approach can be used to examine other related issues such as the impact of formal or informal firm networks on trade
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