Bayesian hierarchical models are increasing popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide f…
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48 results for “Fast Alternating Expectation”
A Fast Algorithm for Computing Expected Loan Portfolio Tranche Loss in the Gaussian Factor Modelmath.NA
We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model. We test it on a 125 name portfolio with a single factor Gaussian model and show that the algorithm gives accurate results. We choose a 125 name portfolio for our tests because this is the size of the standard DJCDX.NA.HY p…
New method explains high-dimensional sphere data with latent factors.
problem Understanding intricate dependence structure in high-dimensional sphere data.
method Exploratory factor analysis of the projected normal distribution with a fast alternating expectation profile conditional maximization algorithm.
result Uniformly excellent results on various data types, including tweets, brain imaging, and cancer gene expression.
We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model. We test it on portfolios ranging in size from 25 (the size of DJ iTraxx Australia) to 100 (the size of DJCDX.NA.HY) with a single factor Gaussian model and show that the algorithm gives accurate results. The algorithm prop…
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally…
Fast convergence of the Expectation Maximization algorithm under a logarithmic Sobolev inequalitystat.ML
New framework improves EM algorithm convergence under log-Sobolev inequality.
problem Improving convergence of the EM algorithm.
method Extending gradient flow techniques to EM algorithm, using free energy representation.
result Exponential convergence of EM algorithm under log-Sobolev inequality.
We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both lo…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo me…
The paper bounds the expectation of empirical processes indexed by Hölder classes.
problem Estimating the expectation of the supremum of empirical processes for distributions on bounded sets.
method Providing upper bounds on the expectation of the supremum of empirical processes indexed by Hölder classes.
result Deriving non-asymptotic risk bounds for estimating distributions using empirical processes and IPM.
New method preserves option structure while using neural networks for volatility.
problem Inconsistent exotic option prices with model calibration.
method Volatility Feature Approach (VFA) using neural networks.
result VFA outperforms model calibration approach for practical volatility surfaces.
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the regression coefficients, and the proposed algorithm jointly learns the low-dimensional s…
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for Symmetric NMF is not as easy as for the nonsymmetric counterpart, the latter adm…
We present an objective function for learning with unlabeled data that utilizes auxiliary expectation constraints. We optimize this objective function using a procedure that alternates between information and moment projections. Our method provides an alternate interpretation of the posterior regularization framework (…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, fo…
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
This paper discusses an alternative explanation for the empirical findings contradicting the positive relationship between risk (variance) and reward (expected return). We show that these contradicting results might be due to the false definition of risk-perception, which we correct by introducing Expected Downside Ris…
Expected Shortfall: a natural coherent alternative to Value at Riskcond-mat.stat-mech
We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representat…
Fast algorithm samples confined polygons efficiently.
problem Sampling confined random equilateral closed polygons efficiently.
method Uses symplectic geometry to sample moment polytope, leading to a linear-time algorithm.
result Explicit formulas for expected distances and total curvature of vertices to the origin.
A concise review of recent few-shot meta-learning methods.
problem Mimicking human fast adaptation to new concepts based on prior knowledge.
method Categorized into four branches based on technical characteristics.
result Current challenges and future prospects identified.
Analog method solves portfolio optimization problems faster and more efficiently.
problem Accurate covariance matrix estimation and fast optimal portfolio selection for financial applications.
method Two-step process using equilibrium propagation and analog Hopfield networks.
result Fully analog pipeline calculates optimal portfolios in energy-efficient manner.
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary time, and we applie…
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nag…
Fast-vollib offers high-performance option pricing and IV computation.
problem Efficiently pricing and computing implied volatility for financial models.
method Open-source Python library with PyTorch, JAX, and CUDA backends, implementing Halley and LBR algorithms.
result High-performance option pricing and IV computation with vectorized implementations.
Study shows how fast a specific matrix completion method works.
problem Completing a rank-one matrix from a subset of revealed entries.
method Alternating minimization approach for matrix completion.
result Polynomial upper bound on convergence rate.
Novel approach for estimating conditional expectations using Bayesian quadrature.
problem Estimating conditional expectations with costly evaluations.
method Probabilistic numerical methods incorporating prior smoothness knowledge.
result Fast convergence rate and uncertainty quantification.
Develops a fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
QEM uses parallel importance weighting for fast approximate Bayesian inference.
problem Bayesian inference challenges in large models with many observations and latent variables.
method Expectation Maximization (EM) with massively parallel importance weighting.
result QEM is faster and more scalable than RWS and VI.
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors, depending on the dimension of the models and the cardinalities of their sample sp…
Simulation of conditional expectations under fast mean-reverting stochastic volatility modelsmath.NA
The paper studies efficient simulation methods for financial firm values under fast mean-reverting volatility.
problem Estimating the probability of firm default under fast mean-reverting stochastic volatility models.
method Approximations using ergodic averages and central limit theorem corrections for efficient simulation.
result Accuracy of approximations assessed through numerical simulation and payoff function estimation.
Paper introduces a new gradient statistic to improve deep learning convergence.
problem Fluctuation effect of gradient updates between iterations.
method Introduces an unbiased stratified statistic \(\bar{G}_{mst}\) and a new algorithm MSSG.
result MSSG algorithm outperforms other sgd-like algorithms in training deep models.
New theory shows how learning algorithms can create a bias towards negative outcomes.
problem Negativity bias in adaptive learning algorithms.
method Generalization of the Hot Stove Effect to settings with negative estimates leading to smaller sample sizes.
result Negativity bias persists even when negative estimates do not lead to avoidance.
Paper presents a fast algorithm for pricing Bermudan swaptions under the two-factor Hull-White model.
problem Evaluating Bermudan swaption prices under the two-factor Hull-White model with high computational efficiency.
method Discretization of expected value calculation, Gaussian kernel sums, fast Gauss transform, grid rotation for stability.
result Significant reduction in computation time and improved stability for correlation close to -1.
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail Expectation describes the expected amount of risk that can be experienced given …
Fast Incremental Expectation Maximization for finite-sum optimization: nonasymptotic convergencecs.LG
FIEM accelerates EM for large datasets with nonasymptotic convergence bounds.
problem Efficiently optimizing large datasets using EM framework.
method FIEM recasts EM in Stochastic Approximation framework and provides nonasymptotic convergence bounds.
result Nonasymptotic bounds for convergence in expectation as a function of and $\kmax$.
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in high-dimensional statistics and signal processing, where the variables often reflect…
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather …
The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.
problem Estimating weights and quality functions in reinforcement learning with function approximation.
method The paper uses minimax methods for estimating marginal importance weights and q-functions.
result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.
In this work we propose a heteroscedastic generalization to RVM, a fast Bayesian framework for regression, based on some recent similar works. We use variational approximation and expectation propagation to tackle the problem. The work is still under progress and we are examining the results and comparing with the prev…
New method speeds up Gaussian process training and inference for large datasets.
problem Training and inference in Gaussian processes are computationally expensive for large datasets.
method Iterative alternating projection method that accesses subblocks of the kernel matrix, reducing time and space complexity.
result Empirically, the method accelerates GP training and inference by up to 72x compared to conjugate gradients.
This work investigates square loss in overparametrized neural networks, revealing its advantages in robustness and calibration.
problem Theoretical understanding of square loss in overparametrized neural networks.
method Systematic investigation of square loss in the NTK regime for both separable and non-separable classes.
result Square loss shows fast convergence rates and robustness guarantees for overparametrized neural networks.
Efficient algorithm finds fast Transformer models.
problem Slow inference time of Transformer models.
method Decompose Transformer architecture into components, use sampling-based one-shot search.
result Achieved 10% to 30% speedup on pre-trained BERT and 70% on top of a previous state-of-the-art model.
Fast classification for sparse models, even with correlated features.
problem Sparse classification with many correlated features.
method Linear and quadratic surrogate cuts, priority queue, and analytical solution for exponential loss.
result 2 to 5 times faster than previous approaches, interpretable models with comparable accuracy.
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
Introduces alternators for modeling sequences, outperforming baselines.
problem Modeling complex sequential data with stability and efficiency.
method Two neural networks (OTN and FTN) alternate between outputting samples in observation and feature spaces, learned via cross-entropy criterion.
result Alternators outperform strong baselines in various domains (Lorenz equations, Neuroscience, Climate Science).
New method improves community detection for large networks.
problem Inefficient community detection for large sparse networks.
method Decouples row and column labels in likelihood function for fast alternating maximization.
result Strongly consistent estimates of communities with provable convergence guarantee.
Network Maximal Correlationstat.ML
We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products between transformed variables. For finite discrete and jointly Gaussian random vari…
Moate Simulation improves accuracy and speed of financial derivative pricing.
problem Efficiently pricing financial derivatives with high accuracy.
method Discrete time simulation of probability distributions using Moate Simulation.
result Moate Simulation provides highly accurate distributions for financial derivatives pricing.