Docent: A content-based recommendation system to discover contemporary art

Recommendation systems have been widely used in various domains such as music, films, e-shopping etc. After mostly avoiding digitization, the art world has recently reached a technological turning point due to the pandemic, making online sales grow significantly as well as providing quantitative online data about artists and artworks. In this work, we present a content-based recommendation system on contemporary art relying on images of artworks and contextual metadata of artists. We gathered and annotated artworks with advanced and art-specific information to create a completely unique database that was used to train our models. With this information, we built a proximity graph between artworks. Similarly, we used NLP techniques to characterize the practices of the artists and we extracted information from exhibitions and other event history to create a proximity graph between artists. The power of graph analysis enables us to provide an artwork recommendation system based on a combination of visual and contextual information from artworks and artists. After an assessment by a team of art specialists, we get an average final rating of 75% of meaningful artworks when compared to their professional evaluations.Comment: submitted to NeurIPS202

Crises de liquidité endogènes dans les marchés financiers

Recent empirical analyses have revealed the existence of the Zumbach effect. This discovery has led to the development of quadratic Hawkes processes, which are suitable for reproducing this effect. Since this model is not linked with the price formation process, we extended it to order book modeling with a generalized quadratic Hawkes process (GQ-Hawkes). Using market data, we showed that there is a Zumbach-like effect that decreases future liquidity. Microfounding the Zumbach effect, it is responsible for a destabilization of financial markets. Moreover, the exact calibration of a GQ-Hawkes process tells us that the markets are on the verge of criticality. This empirical evidence therefore prompted us to analyse an order-book model constructed upon a Zumbach-like feedback. We therefore introduced the quadratic Santa Fe model and proved numerically that there is a phase transition between a stable market and an unstable market subject to liquidity crises. Thanks to a finite size scaling we were able to determine the critical exponents of this transition, which appears to belong to a new universality class. As this was not analytically tractable, it led us to introduce simpler models to describe liquidity crises. Setting aside the microstructure of the order book, we obtain a class of spread models where we computed the critical parameters of their transitions. Even if these exponents are not those of the quadratic Santa Fe transition, these models open new horizons for modelling spread dynamics. One of them has a non-linear coupling that reveals a metastable state. This elegant alternative scenario does not need critical parameters to obtain an unstable market, even if the empirical evidence is not in its favour. Finally, we looked at the order book dynamics from another point of view: the reaction-diffusion one. We have modelled a liquidity that appears in the order book with a certain frequency. The resolution of this model at equilibrium reveals that there is a condition of stability on the parameters beyond which the order book empties completely, corresponding to a liquidity crisis. By calibrating it on market data we were able to qualitatively analyse the distance to this unstable region.De récentes analyses empiriques ont révélé l'existence de l'effet Zumbach. Cette découverte a conduit à l'élaboration des processus de Hawkes quadratique, adapté pour reproduire cet effet. Ce modèle ne faisant pas de lien avec le processus de formation de prix, nous l'avons étendu au carnet d'ordres avec un processus de Hawkes quadratique généralisé (GQ-Hawkes). En utilisant des données de marchés, nous avons montré qu'il existe un effet de type Zumbach qui diminue la liquidité future. Microfondant l'effet Zumbach, il est responsable d'une potentielle déstabilisation des marchés financiers. De plus, la calibration exacte d'un processus GQ-Hawkes nous indique que les marchés sont aux bords de la criticité. Ces preuves empiriques nous ont donc incité à faire une analyse d'un modèle de carnet d'ordres construit avec un couplage de type Zumbach. Nous avons donc introduit le modèle de Santa Fe quadratique et prouvé numériquement qu'il existe une transition de phase entre un marché stable et un marché instable sujet à des crises de liquidité. Grâce à une analyse de taille finie nous avons pu déterminer les exposants critiques de cette transition, appartenant à une nouvelle classe d'universalité. N'étant pas analytiquement soluble, cela nous a conduit à introduire des modèles plus simples pour décrire les crises de liquidités. En mettant de côté la microstructure du carnet d'ordres, nous obtenons une classe de modèles de spread où nous avons calculé les paramètres critiques de leurs transitions. Même si ces exposants ne sont pas ceux de la transition du Santa Fe quadratique, ces modèles ouvrent de nouveaux horizons pour explorer la dynamique de spread. L'un d'entre eux possède un couplage non-linéaire faisant apparaître un état métastable. Ce scénario alternatif élégant n'a pas besoin de paramètres critiques pour obtenir un marché instable, même si les données empiriques ne sont pas en sa faveur. Pour finir, nous avons regardé la dynamique du carnet d'ordres sous un autre angle: celui de la réaction-diffusion. Nous avons modélisé une liquidité qui se révèle dans le carnet d'ordres avec une certaine fréquence. La résolution de ce modèle à l'équilibre révèle qu'il existe une condition de stabilité sur les paramètres au-delà de laquelle le carnet d'ordres se vide totalement, correspondant à une crise de liquidité. En le calibrant sur des données de marchés nous avons pu analyser qualitativement la distance à cette région instable

Endogenous liquidity crises in financial markets

De récentes analyses empiriques ont révélé l'existence de l'effet Zumbach. Cette découverte a conduit à l'élaboration des processus de Hawkes quadratique, adapté pour reproduire cet effet. Ce modèle ne faisant pas de lien avec le processus de formation de prix, nous l'avons étendu au carnet d'ordres avec un processus de Hawkes quadratique généralisé (GQ-Hawkes). En utilisant des données de marchés, nous avons montré qu'il existe un effet de type Zumbach qui diminue la liquidité future. Microfondant l'effet Zumbach, il est responsable d'une potentielle déstabilisation des marchés financiers. De plus, la calibration exacte d'un processus GQ-Hawkes nous indique que les marchés sont aux bords de la criticité. Ces preuves empiriques nous ont donc incité à faire une analyse d'un modèle de carnet d'ordres construit avec un couplage de type Zumbach. Nous avons donc introduit le modèle de Santa Fe quadratique et prouvé numériquement qu'il existe une transition de phase entre un marché stable et un marché instable sujet à des crises de liquidité. Grâce à une analyse de taille finie nous avons pu déterminer les exposants critiques de cette transition, appartenant à une nouvelle classe d'universalité. N'étant pas analytiquement soluble, cela nous a conduit à introduire des modèles plus simples pour décrire les crises de liquidités. En mettant de côté la microstructure du carnet d'ordres, nous obtenons une classe de modèles de spread où nous avons calculé les paramètres critiques de leurs transitions. Même si ces exposants ne sont pas ceux de la transition du Santa Fe quadratique, ces modèles ouvrent de nouveaux horizons pour explorer la dynamique de spread. L'un d'entre eux possède un couplage non-linéaire faisant apparaître un état métastable. Ce scénario alternatif élégant n'a pas besoin de paramètres critiques pour obtenir un marché instable, même si les données empiriques ne sont pas en sa faveur. Pour finir, nous avons regardé la dynamique du carnet d'ordres sous un autre angle: celui de la réaction-diffusion. Nous avons modélisé une liquidité qui se révèle dans le carnet d'ordres avec une certaine fréquence. La résolution de ce modèle à l'équilibre révèle qu'il existe une condition de stabilité sur les paramètres au-delà de laquelle le carnet d'ordres se vide totalement, correspondant à une crise de liquidité. En le calibrant sur des données de marchés nous avons pu analyser qualitativement la distance à cette région instable.Recent empirical analyses have revealed the existence of the Zumbach effect. This discovery has led to the development of quadratic Hawkes processes, which are suitable for reproducing this effect. Since this model is not linked with the price formation process, we extended it to order book modeling with a generalized quadratic Hawkes process (GQ-Hawkes). Using market data, we showed that there is a Zumbach-like effect that decreases future liquidity. Microfounding the Zumbach effect, it is responsible for a destabilization of financial markets. Moreover, the exact calibration of a GQ-Hawkes process tells us that the markets are on the verge of criticality. This empirical evidence therefore prompted us to analyse an order-book model constructed upon a Zumbach-like feedback. We therefore introduced the quadratic Santa Fe model and proved numerically that there is a phase transition between a stable market and an unstable market subject to liquidity crises. Thanks to a finite size scaling we were able to determine the critical exponents of this transition, which appears to belong to a new universality class. As this was not analytically tractable, it led us to introduce simpler models to describe liquidity crises. Setting aside the microstructure of the order book, we obtain a class of spread models where we computed the critical parameters of their transitions. Even if these exponents are not those of the quadratic Santa Fe transition, these models open new horizons for modelling spread dynamics. One of them has a non-linear coupling that reveals a metastable state. This elegant alternative scenario does not need critical parameters to obtain an unstable market, even if the empirical evidence is not in its favour. Finally, we looked at the order book dynamics from another point of view: the reaction-diffusion one. We have modelled a liquidity that appears in the order book with a certain frequency. The resolution of this model at equilibrium reveals that there is a condition of stability on the parameters beyond which the order book empties completely, corresponding to a liquidity crisis. By calibrating it on market data we were able to qualitatively analyse the distance to this unstable region

Endogenous Liquidity Crises

21 pages, 11 figures, 1 tableInternational audienceEmpirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability

Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events

17 pages, 9 figures, 3 tablesInternational audienceWe propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities

From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

18 pages, 6 figuresInternational audienceWe analyse the dynamics of fishing vessels with different home ports in an area where these vessels, in choosing where to fish, are influenced by their own experience in the past and by their current observation of the locations of other vessels in the fleet. Empirical data from the boats near Ancona and Pescara shows stylized statistical properties that are reminiscent of Kirman and F\"ollmer's ant recruitment model, although with two ant colonies represented by the two ports. From the point of view of a fisherman, the two fishing areas are not equally attractive, and he tends to prefer the one closer to where he is based. This piece of evidence led us to extend the original ants model to a situation with two asymmetric zones and finite resources. We show that, in the mean-field regime, our model exhibits the same properties as the empirical data. We obtain a phase diagram that separates high and low herding regimes, but also fish population extinction. Our analysis may have interesting policy implications for the ecology of fishing areas

How does latent liquidity get revealed in the limit order book?

International audienceLatent order book models have allowed for significant progress in our understanding of price formation in financial markets. In particular they are able to reproduce a number of stylized facts, such as the square-root impact law. An important question that is raised-if one is to bring such models closer to real market data-is that of the connection between the latent (unobservable) order book and the real (observable) order book. Here we suggest a simple, consistent mechanism for the revelation of latent liquidity that allows for quantitative estimation of the latent order book from real market data. We successfully confront our results to real order book data for over a hundred assets and discuss market stability. One of our key theoretical results is the existence of a market instability threshold, where the conversion of latent order becomes too slow, inducing liquidity crises. Finally we compute the price impact of a metaorder in different parameter regimes

Schrödinger's ants: A continuous description of Kirman's recruitment model

International audienceWe show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl-Teller (tan 2) potential. Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the "spontaneous conversion" rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of hypergeometric functions

By Force of Habit: Self-Trapping in a Dynamical Utility Landscape

7 pages, 4 figures, 1 tableInternational audienceHistorically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory e↵ects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing e↵ects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour