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.
A new covariance estimator reduces dimensionality and improves portfolio forecasting.
problem Estimating high-dimensional covariance matrices with weak factors.
method Sparse Approximate Factor (SAF) model with l1-regularization. result SAF estimator outperforms other methods in portfolio forecasting.
A new framework approximates covariance matrices using tree decompositions.
problem Approximating covariance matrices for Gaussian distributions.
method Cascade of tree decompositions with Cholesky factorization.
result The proposed framework guarantees convergence and outperforms KL divergence.
Develops a monitoring procedure to detect changes in large approximate factor models.
problem Detecting structural changes in large approximate factor models.
method Randomises the test statistic to create a sequence of i.i.d. statistics for monitoring changes.
result Very small probability of false detections and tight detection times of change-points.
New insights into belief propagation and Bethe approximation for factor graphs.
problem Understanding the correctness and efficiency of belief propagation and its relation to partition functions.
method Viewing factor graphs through the lens of polynomials and reformulating Bethe approximation as a polynomial optimization problem.
result For bipartite normal factor graphs, the Bethe approximation is a lower bound to the partition function under certain analytic conditions.
In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for European option prices. We introduce the notion of modified Black-Scholes price. We …
Efficiently learns Single-Index Models with constant factor approximation.
problem Learning Single-Index Models under L22 loss with unknown link functions. method An efficient algorithm using alignment sharpness for optimization.
result Achieves constant factor approximation to optimal loss for various distributions and link functions.
Proposes new models to solve portfolio selection with cardinality constraints using factor models.
problem Solving portfolio selection with cardinality constraints using factor models.
method Developed 0-1 linear models and a minimum edge-weighted clique problem to solve the cardinality constrained portfolio problem.
result Piecewise linear approximation reduces computation time for solving the quadratic problem.
A new NMF model for co-clustering and data approximation.
problem Finding a low rank approximation for nonnegative data.
method Generalizes separability assumption for NMF, proposing Co-Separable NMF (CoS-NMF).
result CoS-NMF outperforms state-of-the-art methods in co-clustering and data approximation.
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
A new optimization method improves deep learning model training speed.
problem Optimizing large models with natural gradient descent.
method Kronecker-factored eigenbasis for diagonal variance approximation.
result Improves optimization speed for deep network architectures.
This paper studies optimal approximation factors in misspecified off-policy RL, identifying key factors under various settings.
problem Understanding optimal approximation factors in misspecified off-policy value function estimation.
method Examined various settings including weighted L2-norm, L∞ norm, state aliasing, and state coverage. result Established optimal asymptotic approximation factors for different norms and identified two instance-dependent factors for L2(μ) norm. We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical approximation due to Choi and Wir…
Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matri…
We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly cross-sectionally correlated or share at least one unobservable common factor. It only requir…
Bayesian tensor factorization approximates a complex tree model.
problem Intractable size of state-transition matrix in Hidden Tree Markov Models.
method Tucker factorization of tensors for probabilistic interpretation.
result New model outperforms existing approximations on tree-structured data tasks.
Paper proposes Walsh-Hadamard Variational Inference for efficient approximate inference in large models.
problem Over-regularization in variational inference for large models.
method Walsh-Hadamard factorization strategies to reduce parameterization, accelerate computations, and increase posterior expressiveness.
result Efficient approximate inference achieved in over-parameterized models.
Deep model learns complex latent codes without assuming factor structure.
problem Learning latent codes with complex, non-factorial distributions.
method Deep generative factor analysis with beta process prior and stochastic EM algorithm.
result Preliminary results show model can approximate complex distributions.
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
New model reduces matrix factorization bias, yielding truly low-rank solutions.
problem Gradient descent's implicit bias in matrix factorization.
method Introducing a new factorization model with constrained factors and diagonal components.
result The new model consistently exhibits a strong implicit bias, yielding truly low-rank solutions.
We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the fact…
New algorithms for high-dimensional HMMs reduce complexity by discarding non-local factors.
problem High-dimensional HMMs are computationally expensive to filter and smooth.
method Approximate filtering and smoothing via locality in factor graphs, avoiding exponential cost.
result Error bounds in local total variation norm are dimension-free, improving scalability.
The paper uses Gaussian variational approximation for high-dimensional state space models.
problem High-dimensional state space models with complex covariance structures.
method Gaussian variational approximation with dynamic factor model for reduced covariance structure.
result The approach provides a reduced and conditional independence structure for high-dimensional state vectors.
A new matrix factorization method that approximates data without requiring nonnegativity or convexity.
problem Approximating data matrices without the constraints of nonnegativity or convexity.
method A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix.
result The method allows for approximation of data sets without the usual constraints of nonnegativity or convexity.
A new method for optimizing deep neural networks using TKFAC.
problem Optimizing deep neural networks with second-order methods.
method Proposes Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) for Fisher information matrix approximation.
result TKFAC improves performance on deep network architectures compared to state-of-the-art algorithms.
Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive it…
The Hull-White one factor model is used to price interest rate options. The parameters of the model are often calibrated to simple liquid instruments, in particular European swaptions. It is therefore very important to have very efficient pricing formula for simple instruments. Such a formula is proposed here for Europ…
We consider the problem of identifying current coupons for Agency backed To-be-Announced (TBA) Mortgage Backed Securities. In a doubly stochastic factor based model which allows for prepayment intensities to depend upon current and origination mortgage rates, as well as underlying investment factors, we identify the cu…
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.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
Even in the simple one-factor credit portfolio model that underlies the Basel II regulatory capital rules coming into force in 2007, the exact contributions to credit value-at-risk can only be calculated with Monte-Carlo simulation or with approximation algorithms that often involve numerical integration. As this may r…
We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either explicitly (e.g., through star ratings) or implicitly (e.g., through views or purchas…
New algorithm selects best distribution privately in nearly-linear time.
problem Estimating the best distribution from samples under differential privacy constraints.
method Differentially private algorithm with nearly-linear time complexity and optimal approximation factor.
result Achieves optimal approximation factor of 3 with modest sample complexity increase.
Efficiently factorize tensors in streaming data with coreset selection.
problem Efficiently factorize tensors in streaming data.
method Online filtering and kernelization techniques to select a coreset of vectors.
result CP decomposition of coreset approximates full data tensor decomposition.
Deep models improve factor analysis by capturing non-linearity and interaction effects.
problem Improving factor models to better capture complex asset relationships.
method Developed deep fundamental factor models with uncertainty quantification and hidden layers.
result Generated information ratios approximately 1.5x greater than traditional models.
PSMF factorizes time-varying datasets into a dictionary and time-varying coefficients.
problem Factorizing time-varying and non-stationary datasets with temporal nonlinearities.
method Probabilistic Sequential Matrix Factorization (PSMF) using nonlinear Gaussian state-space models and approximate extended Kalman filtering.
result PSMF can account for temporal nonlinearities and estimate generic subspace models.
A new model explains asset returns with a single factor, improving cross-sectional performance.
problem Understanding the cross-section of asset returns with complex models.
method Proposes a non-linear single-factor asset pricing model with a nonparametric link function estimated jointly with sieve-based estimators.
result The model delivers superior cross-sectional performance with a low-dimensional approximation of the link function.
Analytical method approximates ELBO gradient in clutter problem.
problem Clutter problem in Bayesian networks with Gaussian likelihood.
method Reparameterization trick, local approximation of likelihood factors.
result Good accuracy and linear computational complexity compared to classical methods.
Study error bounds and optimal schedules for Masked Diffusions with factorized approximations.
problem Analyzing trade-offs between computation and accuracy in Masked Diffusion Models.
method Provided general error bounds and identified optimal schedules based on data distribution information profiles.
result Identified optimal schedule sizes for Masked Diffusion Models.
We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL dive…
The paper designs multi-factor models for rough volatility, making them easier to simulate.
problem Efficient simulation of rough volatility models due to their non-Markovian and non-semimartingale nature.
method Designs tractable multi-factor stochastic volatility models with Markovian structure.
result Derives a numerical method for solving fractional Riccati equations in rough Heston models.
We develop a fast inference method for non-conjugate Gaussian process models on spike count data.
problem Non-Gaussian spike count data complicates Gaussian Process Factor Analysis.
method We introduce Polynomial Approximate Log-Likelihood (PAL) estimators for non-conjugate GPFA models.
result PAL estimators achieve fast and accurate extraction of latent structure from spike train data.
Bayesian online learning method improves neural network performance.
problem Overcoming catastrophic forgetting in neural networks.
method Kronecker factored online Laplace approximation for Bayesian online learning.
result Achieves over 90% test accuracy across 50 MNIST tasks.
Develops a new model for collateral choice options under stochastic rates.
problem Challenges in quantifying the value of collateral choice options under stochastic rates.
method Develops a scalable and stable stochastic model of collateral spreads under conditional independence, using a common factor approximation.
result Second order model yields accurate results for the value of the collateral choice option.
Optimizes investment portfolios with multiple correlated volatility factors.
problem Maximizing utility in a stochastic environment with multiple correlated volatility factors.
method Perturbation technique around perfectly correlated factors, reducing to single factor problem; numerical solution of linear equations.
result Approximation method reduces complexity of fully non-linear HJB equation to linear equations in lower dimension.
Develops a method for causal inference with noisy confounders.
problem Noisy measurements of confounders in treatment effects models.
method Local principal subspace approximation combining K-nearest neighbors matching and PCA.
result Estimators of treatment effects and counterfactual distributions are constructed.
We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting met…
The paper analyzes how factorized Gaussian approximations underestimate uncertainty in variational inference.
problem Underestimation of uncertainty in variational inference using factorized Gaussian approximations.
method Examined the trade-off between shrinkage and delinking in approximating a Gaussian with a diagonal covariance matrix.
result Entropy of the factorized Gaussian approximation underestimates both componentwise variance and entropy of the original Gaussian.