A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.
A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that t…
A new model for point processes without intensity function trade-offs.
Upper bound on expected supremum of Bernoulli process.
The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
Proposes Gaussian process priors on graph sets with geometric structure.
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization.…
New scalable variational Bayes methods for Hawkes processes.
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enforce the martingale pricing requirement. The martingale condition is i…
This study examines Gaussian processes on Riemannian manifolds and proves contraction rates.
Zellner (1988) modeled statistical inference in terms of information processing and postulated the Information Conservation Principle (ICP) between the input and output of the information processing block, showing that this yielded Bayesian inference as the optimum information processing rule. Recently, Alemi (2019) re…
Vecchia approximations provide the best accuracy-runtime trade-off for Gaussian process approximations.
We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined as probability distributions over all subsets $S\in 2^…
The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.
The paper improves Gaussian process regression by optimizing hyperparameters.
Enhances neural processes for better context handling.
We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approxima…
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to…
Proposes LSGP for better graph signal representation.
Dividing local Gaussian processes improve real-time prediction efficiency.
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers via a Poisson point process with mean measure on the power set of . Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
We characterize value functions in partially observable MDPs as semi-algebraic sets.
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a p…
Paper introduces statistical learning for point processes.
The paper identifies a 'small' set of functions containing Gaussian process samples.
Graph Gaussian processes use Matérn models for better function learning.
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…
Study the limits of discrete DPPs to continuous DPPs as set size grows.
In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a …
Reduces bounded loss learning to binary classification.
New Gaussian processes for Riemannian manifolds enable uncertainty quantification.
We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma pr…
Reduces test set maintenance effort by 80-100%.
We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process in the game). Such a result helps people connect the robust Dynkin game with second-order doubly refle…
We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds …
Develops methods to select informative conformal prediction sets with FCR control.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
GNP models predictive correlations and outperforms NPs.
New method for non-arbitrage pricing in risky assets.
Simplified DGPs training by fixing inducing inputs to subset of data.
The paper develops divergences for Gaussian processes and RKHS settings.
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for effici…
Paper uses neural networks to predict NOx emissions from gas turbines.
A new method combines Gaussian Processes to optimize under uncertainty.
New method scales Gaussian processes with derivatives using variational inference.