In this report, we review the calculation of entropy-regularised Wasserstein loss introduced by Cuturi and document a practical implementation in PyTorch. Code is available at https://github.com/t-vi/pytorch-tvmisc/blob/master/wasserstein-distance/Pytorch_Wasserstein.ipynb
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Python package for estimating Hurst exponent in fBm.
problem Estimating Hurst exponent in fractional Brownian motion.
method Whittle's likelihood method applied to fractional Gaussian noise.
result Implementation achieves state-of-the-art accuracy and speed.
There is a recent interest in neural network (NN)-based communication algorithms which have shown to achieve (beyond) state-of-the-art performance for a variety of problems or lead to reduced implementation complexity. However, most work on this topic is simulation based and implementation on specialized hardware for f…
FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulaeq-fin.PR
We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price contracts with cash flows and/or collateral accounts expressed in foreign currenc…
Marketing analytics is a diverse field, with both academic researchers and practitioners coming from a range of backgrounds including marketing, expert systems, statistics, and operations research. This paper provides an integrative review at the boundary of these areas. The aim is to give researchers in the intelligen…
Gluon optimizes LMO-based methods for large-scale tasks, improving performance and theory-practice gap.
problem LMO-based methods lack theoretical support for practical implementation and smoothness assumptions.
method Introduces Gluon, a new LMO-based method with refined smoothness model.
result Gluon's theoretical stepsizes match fine-tuned values, closing the theory-practice gap.
We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a …
New method for robust fixed-point smoothing without state augmentation.
problem Estimating initial states in Gaussian smoothing algorithms.
method Cholesky-based formulation without state augmentation.
result Matches runtime and robustness of existing methods.
Simplified approach to portfolio risk management and hedging in practice.
problem Challenges in applying academic portfolio risk management and hedging in real-world business settings.
method A straightforward approach using convex optimization and quadratic programming.
result Demonstrates how to solve portfolio risk management and hedging problems with CVXOPT.
We consider the Lipschitz bandit optimization problem with an emphasis on practical efficiency. Although there is rich literature on regret analysis of this type of problem, e.g., [Kleinberg et al. 2008, Bubeck et al. 2011, Slivkins 2014], their proposed algorithms suffer from serious practical problems including extre…
Balls-and-Bins sampling improves DP-SGD privacy and utility.
problem Improving privacy and utility in DP-SGD implementations.
method Introducing Balls-and-Bins sampling as an alternative to shuffling in DP-SGD.
result Balls-and-Bins sampling achieves utility comparable to shuffling while offering better privacy amplification.
A practical guide to Variational Bayes methods.
problem Bayesian inference for data analysis practitioners.
method Explains and demonstrates commonly used Variational Bayes methods.
result Quick derivation and implementation of VB algorithms.
Develops a method to optimize tax codes with practical constraints.
problem Translating optimal taxation theory into practical tax codes.
method Constrained optimization framework for piecewise linear tax functions.
result Generates reforms that meet theoretical and practical constraints.
We consider the problem of online planning in a Markov Decision Process when given only access to a generative model, restricted to open-loop policies - i.e. sequences of actions - and under budget constraint. In this setting, the Open-Loop Optimistic Planning (OLOP) algorithm enjoys good theoretical guarantees but is …
Survey of Bayesian learning for neural networks.
problem Limitations of Bayesian learning in practical applications.
method Introduction to Bayesian Neural Networks and algorithms for inference.
result Discussion of standard and recent approaches for Bayesian inference in neural networks.
To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative metho…
Deep latent variable models have seen recent success in many data domains. Lossless compression is an application of these models which, despite having the potential to be highly useful, has yet to be implemented in a practical manner. We present `Bits Back with ANS' (BB-ANS), a scheme to perform lossless compression w…
Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist that approximate this objective, but they have no provable guarantees. Recently, a…
Algorithm compares Legendrian knots efficiently in some cases.
problem Comparing Legendrian knots efficiently.
method Constructs an algorithm to decide knot equivalence, bypassing time-consuming parts when symmetry is known.
result Efficient comparison possible in many cases with known symmetry.
At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price,...). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose …
Bayesian methods improve causal effect estimation, offering shrinkage and sensitivity analysis.
problem Improving causal effect estimation in practical settings.
method Parametric and nonparametric Bayesian approaches.
result Priors induce shrinkage and sparsity in parametric models.
This report provides an introduction to some Machine Learning tools within the most common development environments. It mainly focuses on practical problems, skipping any theoretical introduction. It is oriented to both students trying to approach Machine Learning and experts looking for new frameworks.
Paper relaxes the Lipschitz constraint in WGANs to improve performance.
problem WGANs do not always outperform other GAN variants due to imperfect implementation of the Lipschitz condition.
method Proposes a new dual form of Wasserstein distance (Sobolev duality) that relaxes the Lipschitz constraint but maintains gradient property.
result SWGAN, based on Sobolev duality, outperforms existing methods in experiments.
Study validates numerical method for singular FBSDEs convergence.
problem Solving singular FBSDEs and associated PDEs.
method Particles approximation for transport operator and tree approximation for diffusion operator.
result Convergence rate of numerical method proved under reasonable conditions.
We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical domains, including biology and architecture. Existing techniques assume the vectors to …
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Modelsstat.CO
This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm …
This chapter focuses on developing datasets for machine learning, addressing data preparation challenges.
problem Challenges in collecting and transforming data for practical machine learning applications.
method Detailed process of dataset development including data collection, transformation, quality evaluation, and distribution.
result Provides insights and practical tools for effective dataset development and management.
New method speeds up PGD for CV robustness evaluation.
problem Computational inefficiency of PGD for robustness evaluation.
method Early termination of PGD based on cycle detection.
result Large speedup factors without sacrificing robustness.
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original variables. Sparse PCA (SPCA) aims to balance statistical fidelity and interpretab…
This study improves audit sampling by using sequential procedures with statistical guarantees.
problem Improving audit efficiency and reliability with statistical methods.
method Formulated as a sequential testing problem, defining null and alternative hypotheses, stopping and decision rules, and exact boundary conditions.
result Exact design yields ex ante control of decision error probabilities, and simulation-based implementation approximates this design.
Adapting functional gradients improves FGD's practicality and theoretical guarantees.
problem Implementing FGD in practice due to infinite-dimensional functional gradients.
method Adapting the representation of functional gradients.
result Establishes convergence to a stationary point for smooth losses and a global minimizer under smoothness + Polyak-Lojasiewicz condition.
Bayesian methods promise to fix many shortcomings of deep learning, but they are impractical and rarely match the performance of standard methods, let alone improve them. In this paper, we demonstrate practical training of deep networks with natural-gradient variational inference. By applying techniques such as batch n…
The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Mean…
NeLLoC improves image compression with parallel decoding.
problem Image compression with OOD generalization.
method Local autoregressive model with parallel decoding.
result Significant gains in compression runtime.
Develops a mathematical model for automatic differentiation in machine learning.
problem Current automatic differentiation lacks a simple mathematical model for machine learning.
method Articulates relationships between program differentiation and nonsmooth functions, provides a class of functions and nonsmooth calculus.
result Shows how nonsmooth calculus applies to stochastic approximation methods and evidence of artificial critical points.
We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substant…
Transcendental Regularization of Finite Mixtures:Theoretical Guarantees and Practical Limitationsstat.ML
TAMD prevents degeneracy in finite mixtures, offering strong guarantees but modest practical improvements.
problem Degeneracy in maximum likelihood estimation of finite mixtures.
method Transcendental regularization with analytic barrier functions.
result Strong theoretical guarantees (identifiability, consistency, robustness) but modest practical improvements.
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations…
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice of a random number generator. The aim of this paper is to provide the tools for…
Unified framework for multi-view autoencoders simplifies model implementation and evaluation.
problem Inconsistent notation and implementation of multi-view autoencoders.
method Unified mathematical framework, documentation, and Python library.
result Comparable or superior performance in benchmarking experiments.
CAE repurposes critics for efficient exploration in RL.
problem Challenges in reinforcement learning, especially exploration.
method Repurposing value networks in RL algorithms for exploration.
result Provably sub-linear regret bounds and strong empirical stability.
We propose a unified methodology to input non-linear views from any number of users in fully general non-normal markets, and perform, among others, stress-testing, scenario analysis, and ranking allocation. We walk the reader through the theory and we detail an extremely efficient algorithm to easily implement this met…
New method AnInfoNCE uncovers latent factors in contrastive learning with practical variability.
problem Theoretical assumptions of contrastive learning loss overlook practical variability in positive pairs.
method AnInfoNCE, a generalization of InfoNCE, models anisotropic variability to uncover latent factors.
result AnInfoNCE increases recovery of latent factors in CIFAR10 and ImageNet, albeit at the cost of accuracy.
We develop a robust convex algorithm to select the regularization parameter in model selection. In practice this would be automated in order to save practitioners time from having to tune it manually. In particular, we implement and test the convex method for -fold cross validation on ridge regression, although the …
This review explores causal decision-making to improve decision quality.
problem Effective decision-making requires understanding causal relationships.
method Causal structure learning, causal effect learning, and causal policy learning.
result Challenges in causal decision-making are identified and recent advances are discussed.
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
Enhances Deep Hedging with K-FAC for financial data.
problem High computational burden in training neural networks for financial applications.
method Integrates Kronecker-Factored Approximate Curvature (K-FAC) optimization with LSTM networks.
result Significant improvements in convergence and hedging efficacy, reducing transaction costs and P&L variance.
Survey on multiplayer bandits, highlighting theoretical gaps and future directions.
problem Theoretical advancements in multiplayer bandits lack practical implementation in real-world scenarios.
method Organizes and contextualizes existing literature on multiplayer bandits.
result Clear directions for future research in adapting theoretical algorithms to real-world situations.