arXiv research

Research simulates Lloyd's of London's specialty insurance market dynamics.

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance. However, there has been little theoretical investigation on the statistical and computatio…

Fair k-means algorithm ensures equitable costs for different groups.

The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster centers from a sketch, i.e. from a drastically compressed representation of the traini…

K-means fails catastrophically in high dimensions, Hartigan's avoids it.

The paper analyzes sterling bills of exchange during the first globalization, revealing their global financial role.

K-bMOM robustly clusters data with outliers, improving on Lloyd-type methods.

Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.

Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to these distortion measures, and they are well-suited for clustering data sampled …

The paper provides convergence bounds for approximating a distribution using point clouds.

This paper analyzes correlations in patterns of trading of different members of the London Stock Exchange. The collection of strategies associated with a member institution is defined by the sequence of signs of net volume traded by that institution in hour intervals. Using several methods we show that there are signif…

New algorithms cluster nodes in SBM graphs faster and more accurately.

Study examines value relevance of oil and gas reserve disclosures in London Stock Exchange.

stCEG models spatial events using Chain Event Graphs in R.

We consider $K$-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering algorithm referred to as networked $K$-means, or $NK$-means, which relies only on l…

Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.

A new method for robust product Markovian quantization overcomes numerical instabilities.

Develops a Bayesian model to predict business revenue and demand.

We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the number of iterations required for convergence. This is achieved by treating the assig…

Paper proposes efficient methods for high-order clustering in tensor block models.

We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large ord…

A method uses Wasserstein clustering to simplify financial data analysis.

Ethereum tackles bribery in blockchain transactions with new fee mechanism.

In recent years, real estate industry has captured government and public attention around the world. The factors influencing the prices of real estate are diversified and complex. However, due to the limitations and one-sidedness of their respective views, they did not provide enough theoretical basis for the fluctuati…

In 2012, JPMorgan accumulated a USD~6.2 billion loss on a credit derivatives portfolio, the so-called `London Whale', partly as a consequence of de-correlations of non-perfectly correlated positions that were supposed to hedge each other. Motivated by this case, we devise a factor model for correlations that allows for…

We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.

We compare some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a portfolio of s…

Trade finance history traced from medieval origins to modern markets.

HSBC grew from Hong Kong to global dominance despite political upheavals.

This appendix proves CORN's universal consistency. One of Bin's PhD thesis examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of London) suggested that CORN is universal and provided sketch proof of Lemma 1.6, which is the key of this proof. Based on the proof in Gyprfi et al. [2006], we thus pro…

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain e…

Recent news cast doubts on London Interbank Offered Rate (LIBOR) integrity. Given its economic importance and the delay with which authorities realize about this situation, we aim to find an objective method in order to detect departures in the LIBOR rate that from the expected behavior. We analyze several interest rat…

We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book tran…

K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as indexing, nearest-neighbor search and prediction, data compression; its beneficial u…

Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step in this direction by developing empirical models that capture behavioral regular…

We showcase how Quantile Regression (QR) can be applied to forecast financial returns using Limit Order Books (LOBs), the canonical data source of high-frequency financial time-series. We develop a deep learning architecture that simultaneously models the return quantiles for both buy and sell positions. We test our mo…

Optimizes clustering in Gaussian mixtures with varying covariance matrices.

A new heuristic LM algorithm improves $k$-segmentation accuracy with less computation.

Let $(M,g)$ be a complete non-compact Riemannian manifold with the $m$-dimensional Bakry-Émery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation \[ u_t=Δu-\n…

We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81-86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. …

In this paper, we study the problem of learning a mixture of Gaussians with streaming data: given a stream of $N$ points in $d$ dimensions generated by an unknown mixture of $k$ spherical Gaussians, the goal is to estimate the model parameters using a single pass over the data stream. We analyze a streaming version of …

Paper defines new risk measures for elliptical distributions.

K-means fails in high dimensions with noise and few samples.

We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function…

For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as $τ^{-α}$ with $α\approx 0.6$, corresponding to a Hurst exponent $H \approx 0.7$. This implies that the signs of future orders are quite predictable from the signs of past orde…

Study gradient estimates for nonlinear parabolic equations on Riemannian manifolds.

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN architecture is based on the composition rules for kernels, so that each unit …