A new method for efficient nested Monte Carlo simulations in financial modeling.
problem Computational challenges in nested stochastic modeling for financial risk assessment.
method Sample recycling approach to speed up inner loop estimations.
result Significantly more efficient than traditional techniques.
The paper proposes an efficient nested simulation design using likelihood ratio method.
problem Designing nested simulations with fixed outer scenarios and minimizing simulation effort.
method Proposes a bi-level optimization problem to decide inner replications and pooling strategies.
result Optimized design achieves $\cO(Γ^{-1})$ mean squared error of estimators.
Optimizes K inner simulations for least-square Monte Carlo to reduce computational cost.
problem Computing conditional expectation E[f (Y)|X] with limited samples.
method Determines optimal number of Y samples (K) for given computational budget.
result Computational gain is maximized when sampling Y given X is inexpensive.
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via VaR or TVaR of a given collection of future economic scenarios representing factor…
Bayesian optimization uses triangulation candidates for better performance.
problem Non-convex and multi-modal optimization challenges in Bayesian optimization.
method Proposes using Delaunay triangulation candidates for discrete search over continuous optimization.
result Triangulation candidates outperform numerically optimized and random alternatives.
Efficient hybrid method for pricing barrier options with stochastic volatility.
problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.
We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive …
Study higher rank inner products and their tilings to describe tori degenerations.
problem Understanding metric degenerations of tori.
method Introduce higher rank inner products and their tilings, use to describe degenerations.
result Describe metric degenerations of polarized tori and Hausdorff limits of tilings.
Characterizes quandles with abelian inner automorphisms.
problem Understanding quandles with specific automorphism properties.
method Generalizes previous work to construct new quandles.
result Homogeneous quandles with abelian inner automorphisms are abelian extensions of trivial quandles.
New spectral functionals for Dirac operators with inner fluctuations computed.
problem Spectral functionals and Dirac operators with inner fluctuations.
method Extension of spectral functionals for Dirac operators with inner fluctuations.
result Computed spectral Einstein functional for Dirac operator with inner fluctuations on even-dimensional spin manifolds.
A new algorithm tackles bilevel optimization with multiple inner minima.
problem Challenges in bilevel optimization with multiple inner minima.
method Reformulated as constrained optimization, solved via primal-dual bilevel optimization (PDBO) algorithm.
result First non-asymptotic convergence guarantee for bilevel optimization with multiple inner minima.
Distillation (Hinton et al., 2015) and privileged information (Vapnik & Izmailov, 2015) are two techniques that enable machines to learn from other machines. This paper unifies these two techniques into generalized distillation, a framework to learn from multiple machines and data representations. We provide theoretica…
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
This paper constructs quandles with abelian inner automorphism groups from graphs, proving their homogeneity.
problem Finding quandles with specific automorphism properties.
method Starting from simple graphs, the paper constructs quandles with abelian inner automorphism groups and proves their homogeneity.
result Homogeneous quandles with abelian inner automorphism groups are constructed from vertex-transitive graphs.
Groups with specific properties have vanishing ℓ2-Betti numbers.
problem Understanding ℓ2-Betti numbers for certain groups. method Introduced cheap 1-rebuilding property and used structure theorem of Tucker-Drob.
result First ℓ2-Betti numbers vanish for specified groups. The author reviews his results on locally compact homogeneous spaces with inner metric, in particular, homogeneous manifolds with inner metric. The latter are isometric to homogeneous (sub-)Finslerian manifolds; under some additional conditions they are isometric to homogeneous (sub)-Riemannian manifolds. The class Ω…
Researchers prove inner product recovery is impossible in latent space models.
problem Recovering inner products in latent space models with random geometric graphs.
method Rate-distortion theory applied to Gaussian or spherical latent locations.
result Impossible to recover inner products if dimensionality exceeds nh(p), matching positive results' conditions. We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We emplo…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a dedicated Expectation Maximization (EM) algorithm. The parameters of the hidden logis…
We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base spaces correspond to inner ideals in Jordan pairs. Using that inner ideals in cla…
Paper proposes a new method to optimize feature coordinates for better image classification.
problem Improving feature extraction for better machine learning classification.
method Mutual-energy inner product optimization method.
result The method enhances low-frequency features and suppresses high-frequency noise, leading to better classification results.
The paper challenges the belief that more inner iterations at test time improve performance in implicit deep learning.
problem The performance improvement of implicit deep learning models with increased inner iterations at test time.
method Theoretical analysis of a simple setting, validation on implicit deep learning problems.
result Overparametrization plays a key role; increasing the number of iterations at test time does not improve performance for overparametrized networks.
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding L2 inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlyi…
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis (kernel PCA). Kernel trick is to define a kernel function which relies on the inner-…
A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific m…
ANIL adapts only a subset of parameters, reducing computational cost.
problem Efficiently adapt model parameters in meta-learning.
method Adapts only a small subset of parameters in the inner loop of ANIL.
result Theoretical convergence and computational complexity analysis for ANIL.
Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.
problem Bounding the index of codimension 2 minimal submanifolds.
method Second inner variation of energy, convergence of energy measures, and stress-energy tensors.
result Bound the Morse index of the submanifold by the index of critical points.
We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …
Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker with many or few ``friends'' who can reliably loan money or stock to him is quit…
New method improves zeroth-order stochastic optimization with adaptive sampling.
problem Optimization problems without gradient information.
method Adaptive sampling quasi-Newton method using finite differences.
result Significant improvement in performance with adaptive sample sizes.
Study on singularities of specific polynomial functions.
problem Characterizing the topology of singularities of mixed functions.
method Introduced inner non-degenerate mixed functions and used Newton boundary to characterize links.
result Links of singularities can be completely characterized under certain conditions.
Graphs with stronger curvature grow faster.
problem Understanding volume growth on graphs with various curvatures.
method Examined inner-outer and Ricci-Ollivier curvatures to relate them to volume growth.
result Graphs with stronger inner-outer curvature growth have faster volume growth.
We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in Cn.
We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively n…
Study on kernel regression risk in high dimensions using Pinsker bound.
problem Kernel regression risk in high-dimensional inner product spaces.
method Investigation of Pinsker bound for kernel regression on sphere Sd with sample size n=αdγ(1+od(1)). result Exact minimax risk and Pinsker constant identified for kernel regression.
The paper solves the Andreadakis problem for specific groups using inner automorphisms.
problem Solving the Andreadakis problem for specific groups.
method Generalizing tools from [Dar19b] to study subgroups of IAn, focusing on the behavior of the Andreadakis problem with inner automorphisms.
result The Andreadakis equality holds for the pure braid group and the mapping class group of the n-punctured sphere.
Proposes new attribution methods for trees with regularization.
problem Feature attribution for trees trained with regularization.
method Prediction Decomposition Attribution (PreDecomp) and TreeInner.
result TreeInner shows state-of-the-art feature selection performance.
INDEQS: A Graph-Based Neural Controlled Differential Equation Framework for Forecasting
problem Forecasting time series with neural networks
method Incorporating prior knowledge of a directed graph
result Outer informedness consistently improves forecasting accuracy
Convex learning for diverse invariances in semi-inner-product space.
problem Efficiently learning invariant representations for a wide range of invariances.
method Developed a convex representation learning algorithm for generalized invariances modeled as semi-norms, introducing Euclidean embeddings for kernel representers in a semi-inner-product space.
result Accurate invariant representations learned efficiently and effectively, validated by experiments.
We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…
This paper speeds up PDV model calibration by learning SPX and VIX prices.
problem Slow calibration of the 4-factor PDV model due to expensive outer simulation.
method Learning SPX and VIX prices with neural networks to reduce outer simulation time.
result Calibration times reduced to just a few seconds.
Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.
problem Formation of naked singularities in Einstein-scalar field system without symmetry assumptions.
method Employing four-type differences and scale-invariant weighted norms to control geometry.
result Global naked singularity structure with incomplete future null infinity and singular inner Cauchy horizon.
In this paper, we develop a loop group description of harmonic maps F:M→G/K ``of finite uniton type", from a Riemann surface M into inner symmetric spaces of compact or non-compact type. This develops work of Uhlenbeck, Segal, and Burstall-Guest to non-compact inner symmetric spaces. To be mo…
Method selects interpretable circular coordinates from data.
problem Abstract circular coordinates are hard to interpret.
method Minimum-weight basis problem in vector matroid for selecting interpretable circle-valued coordinates.
result Proves consistency of cochain inner product estimator.
We investigate the problem of computing a nested expectation of the form P[E[X∣Y]≥0]=E[H(E[X∣Y])] where H is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfo…
PDA method optimizes neural networks with global convergence rate analysis.
problem Quantitative convergence rate for neural network optimization in mean field regime.
method Particle dual averaging (PDA) method, combining Langevin algorithm and outer loop optimization.
result Established quantitative global convergence for two-layer mean field neural networks.