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.
A multilevel optimization method for constrained problems.
A new multilevel framework speeds up ResNet training.
A method learns to solve multilevel combinatorial problems with two players.
Accelerates MCMC sampling for large-scale problems using machine learning.
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures t…
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…
A new training method uses multilevel minimization for machine learning.
The paper introduces a multilevel initialization method for deep neural networks.
Flexible framework assesses multilevel data group heterogeneity.
This paper tackles fitting multilevel low rank matrices by addressing three problems.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…
We apply multilevel Monte Carlo for option pricing problems using exponential Lévy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergen…
Estimates log marginal likelihood using multilevel Monte Carlo.
Improved multilevel scheme for value-at-risk computation.
The time complexity of support vector machines (SVMs) prohibits training on huge data sets with millions of data points. Recently, multilevel approaches to train SVMs have been developed to allow for time-efficient training on huge data sets. While regular SVMs perform the entire training in one -- time consuming -- op…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and su…
Develops a new weighted Laplacian method for graph problems.
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in th…
Develops a fast algorithm for fitting multilevel factor models.
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training s…
Adaptive Multilevel Splitting improves rare event pricing for financial derivatives.
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multil…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete…
The paper improves Monte Carlo methods for optimization problems.
MUSE provides unbiased stopping estimates for optimal problems.
New estimator reduces nested expectation estimation costs.
Deep neural networks favor symmetric structures, enabling multilevel symmetries.
MLMC boosts Bayesian optimization's look-ahead efficiency.
Paper proposes a new algorithm to reduce derivative pricing computation time.
The paper discusses building ETF risk models using a multilevel classification taxonomy.
In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order . This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…
A new algorithm estimates VaR and ES for financial risks.
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
New neural network models speed up Bayesian multilevel modeling.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
Deep learning models exhibit state-of-the-art performance for many predictive healthcare tasks using electronic health records (EHR) data, but these models typically require training data volume that exceeds the capacity of most healthcare systems. External resources such as medical ontologies are used to bridge the da…
Enhances SBI accuracy with multilevel Monte Carlo for expensive simulators.
Detects anomalies in vector fields without distributional assumptions.
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst…
This work is motivated by the needs of predictive analytics on healthcare data as represented by Electronic Medical Records. Such data is invariably problematic: noisy, with missing entries, with imbalance in classes of interests, leading to serious bias in predictive modeling. Since standard data mining methods often …
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizin…
Proposes a method for multilevel explanations of black-box models.
Model trains passing events on a bridge using multilevel Gaussian process.
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …
New method estimates nested expectations with biased and antithetic sampling.