arXiv research

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…

A new method detects changes in multivariate data using random forests.

Trading strategy uses Hoeffding's Inequality to predict financial regime change.

Online change detection algorithm using random Fourier features.

New method detects change-points in population genetics.

Software estimates inequality in random systems with changing communities.

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components o…

The paper outlines future work in random sets theory.

Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter the conditional dependence between the random variables, and potentially produce s…

Study reveals trade dynamics in dry bulk shipping networks, highlighting their randomness and periodic changes.

New method robust to random distributional shifts in prediction.

Efficiently infers time-varying sparse MRFs with strong statistical guarantees.

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $τ$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations whi…

A new method for LDA using randomized Kaczmarz improves accuracy for large datasets.

Geometric QHD tests improve hub detection in correlated data.

This chapter covers different approaches to policy evaluation for assessing the causal effect of a treatment or intervention on an outcome of interest. As an introduction to causal inference, the discussion starts with the experimental evaluation of a randomized treatment. It then reviews evaluation methods based on se…

Master algorithm fails to detect non-stationarity in practical settings.

An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art perfor…

New framework to test neural network representation similarity measures.

Financial price changes obey two universal properties: they follow a power law and they tend to be clustered in time. The second regularity, known as volatility clustering, entails some predictability in the price changes: while their sign is uncorrelated in time, their amplitude (or volatility) is long-range correlate…

We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equival…

We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to …

Recent years have seen an increasing popularity of learning the sparse \emph{changes} in Markov Networks. Changes in the structure of Markov Networks reflect alternations of interactions between random variables under different regimes and provide insights into the underlying system. While each individual network struc…

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-mod…

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correla…

The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density $f\left( x\right) \simeq f_{0}x^{-2}$, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability…

In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships …

Boosts change-point detection power with optimal sub-sampling.

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility sur…

Financial markets are not random, but hard to predict due to hidden causes and strategic use.

Learning algorithms need bias to generalize and perform better than random guessing. We examine the flexibility (expressivity) of biased algorithms. An expressive algorithm can adapt to changing training data, altering its outcome based on changes in its input. We measure expressivity by using an information-theoretic …

Volatility, fitting with first order Landau expansion, stationarity, and causality of the Taiwan stock market (TAIEX) are investigated based on daily records. Instead of consensuses that consider stock market index change as a random time series we propose the market change as a dual time series consists of the index a…

Estimates change point in high dimensional time series models.

We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sampl…

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity $+ v$ or $-v$. The changes of direction are governed by an homogeneous Poisso…

Online CPD for weighted and directed graphs using RDPG model.

In Random Forests, proximity distances are a metric representation of data into decision space. By observing how changes in input map to the movement of instances in this space we are able to determine the independent contribution of each feature to the decision-making process. For binary feature vectors, this process …

In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to change with both altitude and velocity. It is thus important to quantify these cha…

The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company's interest to detect the change time as soon as possible in order to re-evaluate a new fair v…

Paper introduces a novel framework for recognizing dynamic ranking structures in preference-based data.

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…

Method finds counterfactual explanations for random forest models.

We develop a mixture procedure for multi-sensor systems to monitor data streams for a change-point that causes a gradual degradation to a subset of the streams. Observations are assumed to be initially normal random variables with known constant means and variances. After the change-point, observations in the subset wi…

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the …

AACC improves RL performance in changing environments.

The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that…

An expanding literature articulates the view that Taylor rules are helpful in predicting exchange rates. In a changing world however, Taylor rule parameters may be subject to structural instabilities, for example during the Global Financial Crisis. This paper forecasts exchange rates using such Taylor rules with Time V…

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors…