Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate expressions for variables h(t) and u(t). We provide here condition for the unique…
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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.
168,694 papers · 148 categories
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48 results for “closed-form evaluation”
New method generates novel samples from closed-form diffusion models.
problem Closed-form SGMs memorize training data and cannot generate novel samples.
method Explicitly smooth closed-form score, use nearest-neighbor estimator.
result Efficient method generates novel samples without training.
A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functi…
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
Closed-form relations and approximations for SE(3) derivatives for robust numerical simulations.
problem Deriving closed-form derivatives and approximations for SE(3) for robust numerical simulations.
method Avoiding block partitioning, deriving higher-order approximations for differential, first and second derivatives, Jacobian, and Hessian.
result Compact and numerically robust closed-form relations for SE(3) derivatives.
Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern comput…
The paper introduces closed-form expressions for interpreting Tsetlin Machines.
problem Interpreting complex Tsetlin Machines with a large number of clauses.
method Developed closed-form expressions for local and global interpretability of Tsetlin Machines.
result The expressions enable real-time feature importance assessment and data clustering.
MDMA provides closed-form marginals and conditionals for deep networks.
problem Lack of closed-form marginals and conditionals in deep neural models.
method MDMA architecture combining deep scalar representations and hierarchical tensor decompositions.
result MDMA outperforms state-of-the-art models in tasks requiring marginalization and conditional inference.
In recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite …
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
Proposes a new method for data assimilation using closed-form conditional diffusion models.
problem Data assimilation for systems with complex, non-Gaussian probability distributions.
method Uses kernel density estimation to model joint distributions and leverages the score function for efficient evaluation.
result Outperforms ensemble Kalman and particle filters in nonlinear data assimilation problems.
We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicabl…
Regression problems that have closed-form solutions are well understood and can be easily implemented when the dataset is small enough to be all loaded into the RAM. Challenges arise when data is too big to be stored in RAM to compute the closed form solutions. Many techniques were proposed to overcome or alleviate the…
VBphenoR uses variational Bayes for EHR-based patient phenotyping.
problem Phenotyping patients from EHR data for targeted treatments.
method Variational Bayes Gaussian Mixture Model (GMM) and logistic regression.
result Closed-form inference for efficient patient phenotype determination.
We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the averag…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be ev…
Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributio…
In this paper, we model financial markets with semi-Markov volatilities and price covarinace and correlation swaps for this markets. Numerical evaluations of vari- nace, volatility, covarinace and correlations swaps with semi-Markov volatility are presented as well. The novelty of the paper lies in pricing of volatilit…
SDE automatically recovers interpretable discrete distributions.
problem Limited interpretable discrete probability laws.
method Unsupervised framework using symbolic density estimation.
result Accurately recovers interpretable discrete distributions.
Alternative closed-form formula for spread call option prices under log-normal models.
problem Valuation of spread call options under log-normal models.
method Developed an alternative closed-form formula for spread call option prices.
result Our formula performs better for certain range of model parameters than existing closed-form formula.
We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points. Unlike former approaches, we obtain closed-form updates based on natural gradients that lead to efficient optimization. We evaluate the algorithm on real-world datasets containing up…
We solve the mean parametrization of von Mises-Fisher distribution.
problem No closed-form normalization function for mean parameters exists.
method Derived a second-order ODE for mean normalizer and provided approximations.
result Rapid evaluation of densities and natural parameters in terms of mean parameters.
A new metric for comparing probability measures on graphs, scalable and negative definite.
problem Optimal transport's high complexity and indefiniteness for kernel machines.
method Sobolev transport metric for graph metrics, closed-form formula, negative definiteness.
result Sobolev transport yields a scalable and negative definite metric.
A new retraction on Stiefel manifold with a closed-form inverse.
problem Efficiency in Riemannian computing applications.
method Introduces a new retraction on the compact Stiefel manifold with a closed-form inverse.
result The retraction is second-order accurate and features a closed-form inverse.
A new method for inferring latent states in Markov jump processes.
problem Intractable exact inference for Markov jump processes.
method Entropic matching within expectation propagation.
result Superior performance in approximating the mean of the posterior process.
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
Unified view on GP transfer learning for Bayesian optimization.
problem Improving data efficiency in Bayesian optimization with scarce data.
method Unified hierarchical GP models for transfer learning, including a novel boosted GP transfer model.
result Unified analysis and comparison of transfer learning methods for GP models.
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation requires the evaluation of the overshoot/undershoot distributions of the surplus proce…
We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Though the model is non-Markov, there exist…
KL-MS improves regret bounds for multi-armed bandits with bounded rewards.
problem Designing efficient exploration algorithms for multi-armed bandits with bounded rewards.
method Kullback-Leibler Maillard Sampling (KL-MS) for multi-armed bandits with bounded rewards.
result KL-MS achieves a worst-case regret bound of .
Iterative tilting fine-tunes diffusion models for reward-tilted distributions.
problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.
This paper provides a dictionary of closed-form kernel mean embeddings.
problem Challenges in deriving closed-form kernel mean embeddings.
method Comprehensive dictionary and practical tools for deriving new embeddings.
result Provides a Python library with minimal implementations of embeddings.
Based on the concept of self-decomposable random variables we discuss the application of a model for a pair of dependent Poisson processes to energy facilities. Due to the resulting structure of the jump events we can see the self-decomposability as a form of cointegration among jumps. In the context of energy faciliti…
Layer-wise networks have a closed-form solution and a stopping criterion.
problem Training networks one layer at a time without backpropagation.
method Proved the Kernel Mean Embedding as the closed-form solution and developed a stopping criterion.
result Layer-wise networks converge to a highly desirable kernel for classification.
New retraction on symplectic Stiefel manifold with closed-form inverse.
problem Efficient mapping of manifold data to Euclidean domain.
method Introduces a new retraction map with a closed-form inverse.
result The new retraction has a closed-form inverse, unlike previous methods.
Layer-wise networks have a closed-form solution and a stopping criterion.
problem Training networks one layer at a time without backpropagation.
method Proved the closed-form solution using the kernel Mean Embedding and Neural Indicator Kernel.
result Layer-wise networks have a closed-form solution and a stopping criterion.
An extension of the regularized least-squares in which the estimation parameters are stretchable is introduced and studied in this paper. The solution of this ridge regression with stretchable parameters is given in primal and dual spaces and in closed-form. Essentially, the proposed solution stretches the covariance c…
Meta-GLAR combines global deep representations with local adaptation for improved forecasting accuracy.
problem Joint learning from related time series boosts accuracy but fails for out-of-sample forecasting.
method Meta-GLAR uses a meta-learning approach to adapt RNN representations for each time series.
result Meta-GLAR outperforms state-of-the-art methods in out-of-sample forecasting accuracy.
Proposes a method to adapt DNNs to drift in data distribution.
problem Adapting to out-of-distribution data and shifting objectives.
method Bayesian Inference, Variational Density Propagation, Evidence Lower Bound (ELBO), Minimum Description Length (MDL) Principle.
result Minimizes catastrophic forgetting by approximating MDL principle.
Survey on closed-form Fisher-Rao distance expressions.
problem Finding closed-form expressions for Fisher-Rao distance.
method Collect and present examples of closed-form expressions for Fisher-Rao distance of discrete and continuous distributions.
result Presentation of closed-form expressions for Fisher-Rao distance of various distributions.
In this note we consider setups in which variational objectives for Bayesian neural networks can be computed in closed form. In particular we focus on single-layer networks in which the activation function is piecewise polynomial (e.g. ReLU). In this case we show that for a Normal likelihood and structured Normal varia…
Introduces q-paths for generalizing geometric annealing paths in machine learning.
problem Limited applicability of existing path methods in machine learning.
method Develops a family of paths derived from a generalized mean, including geometric and arithmetic mixtures.
result Empirical gains in Bayesian inference and generative model evaluation.
Bayesian neural networks learn weights with closed-form updates.
problem Efficiently learning Bayesian neural networks with closed-form updates.
method Closed-form Bayesian inference for online learning of Gaussian-weighted BNNs.
result Closed-form expressions for sequential/online training of BNNs.
New method uses generative models to estimate aleatoric uncertainty without strict data restrictions.
problem Estimating aleatoric uncertainty with limited data distribution or dimensionality.
method Conditional generative models and two metrics for measuring distributional discrepancies.
result Metrics accurately measure conditional distributional discrepancies and train competitive models.
Improved portfolio optimization using VaR and CVaR with NMVM models.
problem Optimizing portfolios with VaR and CVaR under NMVM distributions.
method Transformed mean-CVaR-skewness problems into quadratic optimization with closed-form solutions for NMVM models.
result Approximate closed-form expressions for VaR and CVaR of NMVM portfolios.
CCC clusters with controlled spread, outperforming standard methods.
problem Compact and structured clustering with spread control.
method Constrained Centroid Clustering using Lagrangian formulation.
result CCC achieves more compact clusters with reduced radial spread.
We consider optimization of composite objective functions, i.e., of the form , where is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we…
In this work, I generalize Merton's approach of pricing risky debt to the case where the interest rate risk is modeled by the CIR term structure. Closed form result for pricing the debt is given for the case where the firm value has non-zero correlation with the interest rate. This extends previous closed form pricing …