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.
FFBO optimizes functions as inputs and outputs, improving on existing BO methods.
Deep, wide ConvResNets can approximate functions and their smoothness.
Paper introduces a method for operator learning using random features.
Bayesian kernel regression improves functional output prediction.
Enhances neural networks with prior function values to improve accuracy.
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Here we use phylogenetic Gaussian process regression to model the evolution of simulated function-valued traits. Given function-valued data only from the tips of an evolutionary tree and utilising independent pri…
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs, computes the lower and upper bound on the function values. Because the network and the …
NP-PROV separates mean and variance spaces to improve function uncertainty.
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used. Our algorithm consists of two steps; one is the direction estimate step and the o…
New method reveals true causal functions in nonlinear time series, not just scores.
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze bandit algorithms for both general and structured nonconvex problems with nonstation…
New kernels capture both local and non-local interactions efficiently.
Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient, Hessian and function value in order to obtain the search direction and adjust the r…
Function trees simplify complex ML models for better understanding.
Framework extends neural operators to handle functions outside training set.
Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popu…
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
Sobolev training helps neural nets fit function values and derivatives.
LUNO linearizes neural operators to quantify their predictive uncertainty.
Sepsis is a poorly understood and potentially life-threatening complication that can occur as a result of infection. Early detection and treatment improves patient outcomes, and as such it poses an important challenge in medicine. In this work, we develop a flexible classifier that leverages streaming lab results, vita…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast to this, multiple model enumeration attracts increasing interests in non-standar…
Study uncovers complex critical points in tensor decomposition.
We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of function values are available, algorithms for -dimensional optimization that use …
Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function, this task can be interpreted as the problem called Level Set Estimation (LSE) --…
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Contin…
The paper analyzes Random Search and introduces BLiN-MOS for bandit learning.
Bayesian optimization (BO) aims to minimize a given blackbox function using a model that is updated whenever new evidence about the function becomes available. Here, we address the problem of BO under partially right-censored response data, where in some evaluations we only obtain a lower bound on the function value. T…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approxima…
This work extends Gaussian process priors to neural operators for function space mappings.
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of non-crossing quantile planes over arbitrarily shaped convex predictor domains in a…
A new one-point feedback scheme improves ZO algorithms for black-box optimization.
This paper conditions non-linear infinite-dimensional diffusion processes.
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher…
Generative models for function-valued data in infinite dimensions.
We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting as optimization with dueling-choice bandits since both direct queries and duels a…
A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalize…
Study pricing options on forward contracts using infinite-dimensional affine models.
New convergence rates for shuffling gradient methods without strong convexity.
New algorithms find near-stationary points in convex optimization.
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables,…
In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm…
Study revisits AdaGrad convergence with relaxed noise assumptions.
The study compares econometric and deep learning models for forecasting COMEX copper futures volatility.
Studied SGD convergence under weak conditions.
New algorithms solve complex minimax problems without needing derivatives.
New method certifies neural network function space norms from point evaluations.
Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known…