Adaptive approximations improve variational inference for complex models.
problem Efficiently approximate marginal distributions and partition functions in complex probabilistic models.
method Two classes of adaptive approximations that include Bethe, tree-reweighted, and convex free energies.
result Proposed approximations automatically adapt to a given model and outperform existing methods.
Approximates call option prices for Barndorff-Nielsen and Shephard model.
problem Calculating exact option prices for complex models is computationally expensive.
method Developed approximate expressions using decomposition formula.
result Approximations are effective as shown by numerical experiments.
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matri…
Transforms offline algorithms to online with low regret in random order model.
problem Developing online algorithms with low approximate regret from offline approximation algorithms.
method General reduction theorem and coreset construction method.
result Achieves polylogarithmic ε-approximate regret for various online problems.
New findings on how convolutional architectures approximate time series data.
problem Understanding the approximation properties of convolutional architectures in time series modeling.
method Mathematical analysis of convolutional architectures applied to time series modeling.
result A new definition of spectrum-based regularity for measuring temporal relationships under convolutional approximation.
The paper develops new methods to approximate ruin probabilities in a perturbed risk model.
problem Calculating exact ruin probabilities in a perturbed risk model is complex.
method Adapted Cramér-Lundberg model with Wiener process, four approximation methods.
result Four approximation methods provide high accuracy for ruin probabilities.
New algorithms for approximating stochastic processes efficiently.
problem Finding accurate finite approximations for stochastic processes.
method Develops new algorithms and fast implementations for approximating stochastic processes.
result Efficient approximations for stochastic processes can be found.
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…
Improved approximations for rough Heston model reduce errors.
problem Lack of Markov and semimartingale properties in rough Heston model.
method Markovian approximations with weak error analysis.
result Super-polynomial convergence of new approximations.
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIB…
We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the a…
Improved calibration of HJM models using small volatility approximation.
problem Calibration issues in HJM models with deterministic correlations and mean reversals.
method Use of Small Volatility Approximation in calibration of Multi-Factor HJM models.
result Calibration quality is very good and independent of the number of factors.
Bayesian method improves approximate model posteriors.
problem Poor uncertainty quantification in approximate Bayesian inference.
method Optimizing a transformation of the approximate posterior to maximize a scoring rule.
result Significant reduction in bias and improvement in posterior coverage properties.
New method for epidemic model inference using multinomial approximations.
problem Inference in stochastic epidemic models with partial observations.
method Recursive multinomial approximations to integrate over unobserved variables.
result Accuracy demonstrated through real and simulated data.
Approximates bond option volatilities using affine short-rate models.
problem Calculating implied volatilities for bond options.
method Derive asymptotic approximation for bond option volatilities under affine short-rate dynamics.
result Accuracy of approximation validated through numerical experiments.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti…
Random feature models approximate functions in Banach spaces efficiently.
problem Approximating functions in Banach spaces efficiently.
method Randomly initialized feature maps and linear readout training.
result Universal approximation in Bochner spaces for Banach space-valued models.
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there i…
This thesis disentangles Gauss-Newton and variational approximations in Bayesian deep learning.
problem Understanding the interplay between the Gauss-Newton method and variational approximations in Bayesian deep learning.
method Analysis of the Gauss-Newton method and Laplace/Gaussian variational approximations for neural networks.
result The combination of the Gauss-Newton method with approximate inference can be cast as inference in a linear or Gaussian process model.
VISA improves inference efficiency for complex models.
problem Efficient approximate inference in computationally intensive models.
method Sequential sample-average approximations within a trust region.
result VISA achieves comparable accuracy with computational savings.
Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some known auxiliary model. Since the resulting approximation formula has closed-form it…
QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.
problem Overconfident out-of-distribution predictions from DNNs.
method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.
result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.
Paper proves GDL models can approximate any continuous function on non-Euclidean data.
problem Processing non-Euclidean data with universal feedforward models.
method Introduces geometric deep learning framework for differentiable manifold geometries.
result GDL models can uniformly approximate any continuous function on compact sets.
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…
The paper approximates CARMA models for option pricing.
problem Approximating the transition density of CARMA(p, q) models.
method Using Gauss-Laguerre quadrature and time changed Brownian Motion.
result Provides an analytical formula for option prices.
We derive caplet volatilities for quadratic models, providing an asymptotic approximation.
problem Calculating caplet volatilities for quadratic term-structure models.
method Asymptotic approximation for caplet volatilities under quadratic models.
result Asymptotic accuracy of the derived caplet volatilities.
Improves hyperparameter learning in GP models with non-conjugate likelihoods.
problem Hyperparameter learning entangled with approximate inference in GP models.
method Hybrid training procedure combining VI for inference and EP-like marginal likelihood approximation for hyperparameter learning.
result Empirically demonstrates the effectiveness of the proposed training procedure across various data sets.
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…
New model classes for function approximation by neural networks defined on domains.
problem Defining novel model classes for function approximation on bounded domains.
method Introducing weighted variation spaces to define new model classes on domains.
result New model classes are strictly larger than classical ones but maintain the same NNA rates.
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. …
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
One of the key approaches to save samples in reinforcement learning (RL) is to use knowledge from an approximate model such as its simulator. However, how much does an approximate model help to learn a near-optimal policy of the true unknown model? Despite numerous empirical studies of transfer reinforcement learning, …
Transformers use ReLUs to approximate softmax efficiently.
problem Analyzing resource usage in softmax transformer models.
method Translating ReLU approximation results to softmax attention mechanisms.
result Economic resource bounds for softmax attention mechanisms.
Method improves deep learning models for datasets with mixed approximate symmetries.
problem Improving deep learning models for datasets with mixed approximate symmetries.
method Regularizer-based approach to build models for datasets with mixed approximate symmetries.
result Our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.
Deviation inequalities for stochastic approximation methods.
problem Establishing bounds on the deviation of stochastic approximation methods.
method Martingale approximation method for separately Lipschitz functions.
result Established various deviation inequalities for stochastic approximation by averaging and minimization.
This work shows how approximate reward models can significantly improve inference-time scaling.
problem Improving the efficiency of inference for large language models.
method Identifying the Bellman error of approximate reward models and using Sequential Monte Carlo (SMC) for inference.
result Approximate reward models can reduce computational complexity from exponential to polynomial in T. We develop a Markovian approximation for SVV models to compute hedging strategies.
problem Computing optimal hedging strategies for SVV models with non-Markovian noise.
method Develop a Markovian approximation of the Volterra noise kernel to compute hedging strategies.
result Error estimates for the approximation of volatility, prices, and optimal hedge.
We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the likelihood in this type of models. However, such approximations can be noisy and c…
Proposes a new method to approximate Bayesian predictive uncertainty.
problem Bayesian uncertainty quantification in model predictions.
method Self-supervised learning approach to approximate posterior predictive distribution.
result SSLA and ASSLA outperform classical Laplace approximations in predictive calibration.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
New iterative methods improve Vecchia-Laplace approximations for large data sets.
problem Inaccurate and slow Vecchia-Laplace approximations for large data sets.
method Iterative methods to improve Vecchia-Laplace approximations, including preconditioners and novel methods for predictive variances.
result Order of magnitude speed-up and threefold increase in prediction accuracy compared to state-of-the-art methods.
This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
problem Learning complex posterior distributions with skewness, multimodality, and bounded support.
method Develops a spline-based nonparametric approximation approach for ADVI.
result Establishes the asymptotic consistency of the derived lower bound for importance weighted autoencoder.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
A new method approximates posterior for VAEs without iterative training.
problem Inference models in VAEs are poor early on, leading to suboptimal models.
method Train generative and inference models independently, using a model-agnostic posterior approximation (MAPA).
result MAPA approximates the true posterior deterministically and can improve density estimation.
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always intractable, most efforts were made on finding an accurate approximation the true post…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. …
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…