This paper investigates Shampoo's heuristics and decouples preconditioner updates.
problem Improving Shampoo's heuristics for training neural networks.
method Decomposing preconditioner updates, correcting eigenvalues, and adapting eigenbasis computation frequency.
result Principled techniques to remove Shampoo's heuristics and improve training algorithms.
Bayesian methods estimate regression functions on submanifolds using graph Laplacian eigenbasis.
problem Estimating regression functions on unknown smooth submanifolds.
method Random geometric graph structure, Bayesian priors based on random basis expansion in graph Laplacian eigenbasis.
result Posterior contraction rates are minimax optimal for any positive smoothness index.
Revisits Gaussian process model with spherical harmonics for scalable deep learning.
problem Scaling Gaussian process models to large input dimensions with high frequency learning.
method Introduces new kernels related to deep models, variational learning of spherical harmonic phases, and sparseness in eigenbasis.
result Enables scaling to larger input dimensions and learning of high frequency variations.
Reducing the test time resource requirements of a neural network while preserving test accuracy is crucial for running inference on resource-constrained devices. To achieve this goal, we introduce a novel network reparameterization based on the Kronecker-factored eigenbasis (KFE), and then apply Hessian-based structure…
Optimization algorithms that leverage gradient covariance information, such as variants of natural gradient descent (Amari, 1998), offer the prospect of yielding more effective descent directions. For models with many parameters, the covariance matrix they are based on becomes gigantic, making them inapplicable in thei…
Paper proposes a statistical test for transfer learning in linear regression.
problem Theoretical framework for parameter transfer in linear regression.
method Developed a statistical test to predict transfer quality.
result The test can predict if a fine-tuned model has lower prediction risk.
The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits also a family of Spinc Dirac operators which has a spectral section (in the sens…
SCaLE tackles dynamic regret in noisy bandit feedback with switching costs.
problem Unbounded metric movement costs in bandit online convex optimization.
method SCaLE algorithm for high-dimensional dynamic quadratic hitting costs and ℓ2-norm switching costs, with spectral regret analysis. result First algorithm achieving sub-linear dynamic regret without hitting cost knowledge.
Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive poste…
New spectral clustering method using LASSO regularization for robust graph partitioning.
problem Lack of theoretical guarantees for spectral clustering on general graph models.
method 1-spectral clustering on a new random model with LASSO regularization.
result Effective and robust to small noise perturbations, validated by simulations and real data.
Simplified kernel ridge regression with a conservation law.
problem Understanding the test risk and generalization of kernel ridge regression.
method Identification of a conservation law that limits KRR's learning ability, leading to simplified expressions for test risk.
result Transparency in test risk expressions through the conserved quantity in the kernel eigenbasis.
The paper studies non-integer curvature flows and proves convergence to spheres under specific conditions.
problem Analyzing the convergence of non-integer curvature flows on rotationally symmetric surfaces.
method Spectral theory of singular Sturm-Liouville operators to construct an eigenbasis and prove convergence.
result The flow converges to a round sphere if the focal points coincide at the poles, otherwise to a non-round Hopf sphere.
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.
We extend Kyle's model to include stochastic liquidity and multiple assets.
problem Modeling informed trading with stochastic liquidity and multiple assets.
method Developed a variational formulation and derived a matrix-valued martingale depth process.
result A linear-Gaussian equilibrium with stochastic matrix-valued price impact.
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors tha…
We develop a framework for analyzing extreme values in correlated financial data.
problem Quantifying and mitigating risk in complex financial systems.
method Developed a practical framework for handling finite, multivariate, and correlated time series in finance.
result We successfully analyze high-frequency stock returns using univariate extreme value tools.
A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.
problem Challenges in spectral positional encodings for directed graphs, including computational complexity and gauge invariance issues.
method Learnable spectral positional encodings of the form hθ(Aq)R, computed in a Hermitian block Krylov subspace from sparse matrix-vector products. result The method is gauge-invariant and converges to the exact eigendecomposition oracle as the depth grows.
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of Rd. On this approximate eigenbasis the eigenvalues of the c…
Quantum mechanics applied to credit loans for better repayment schedules.
problem Improving repayment schedules for credit loans.
method Introducing quantum mechanics concepts to credit loans, defining operators for debt, amortization, interest, and installments, and using SO(M) symmetry to optimize periodic payments.
result Optimized repayment schedules for borrowers without altering lender's earnings.
How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as n−β where n is the number of training examples and β an exponent that depends on both data and algorithm. In this work we measure β when applying kernel methods to real datasets. For …