A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study spectral distribution of twisted Laplacian on high genus hyperbolic surfaces.
New spectral mixture representation for isotropic kernels simplifies random Fourier features.
New theorem improves spectral gap for sampling from mixture distributions.
New estimates show spectral gap stability in RCD spaces, close to Beta distribution.
Study shows non-spectrality of certain curves and line segments.
Optimizes risk measures given known marginal distributions of two unknown factors.
New spectral clustering method for graphs with uneven node degrees.
Despite excellent progress in recent years, mode collapse remains a major unsolved problem in generative adversarial networks (GANs).In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. Theoretical analysis shows that the optimal …
Spectral algorithms improve under covariate shift with novel weighted techniques.
Improved singular value approximation for convolutional layers.
Spectral clustering improves accuracy and efficiency for clustering discrete distributions.
Study tackles distribution shift in combinatorial settings using matrix completion techniques.
A new method for nonstationary Gaussian processes using Fourier features.
Study heavy-tailed weights' impact on neural network's spectral distribution.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
Study uses spectral risk for learning with heavy-tailed data.
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…
We study spectral asymptotics for the Laplace operator on differential forms on a Riemannian foliated manifold equipped with a bundle-like metric in the case when the metric is blown up in directions normal to the leaves of the foliation. The asymptotical formula for the eigenvalue distribution function is obtained. Th…
We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors , we say a set is an -spectral spanner if for all there is a probability distribution supported on such that $$vv^\intercal \preceq α\cdot\m…
Paper tackles functional linear regression using spectral algorithms with discrete observations.
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and convergence rates for distributed SGD to the data distribution instead of the regu…
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
We analyze DMs using spectral methods to design effective noise schedules.
Spectral images captured by satellites and radio-telescopes are analyzed to obtain information about geological compositions distributions, distant asters as well as undersea terrain. Spectral images usually contain tens to hundreds of continuous narrow spectral bands and are widely used in various fields. But the vast…
Refined analysis of Mitra's algorithm for discrete mixtures.
We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user's priorities for model performance.…
New framework detects directional influence in multivariate time series.
Improves regression models' performance on covariate shift.
In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally ne…
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how th…
Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.
The paper analyzes the latent geometry of generative diffusion models.
Consistent spectral clustering with fairness constraints on representation graphs.
Improves learning of spectral mixture kernels with approximate Bayesian inference.
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are available, where current methods fail to handle uncertainty appropriately. In this c…
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…
Paper proposes a new DRL algorithm optimizing Spectral Risk Measures for better risk management.
Spectral clustering identifies clusters of multivariate extremes.
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density fun…
Optimal spectral method found for inhomogeneous spiked Wigner model.
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlyi…
Algorithm identifies fractal system's scaling exponents in high dimensions.
Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation …
Paper analyzes spectral algorithms under covariate shift, providing convergence rates.
In this paper we consider certain asymptotically Euclidean spaces, namely compact manifolds with boundary X equipped with a scattering metric g, as defined by Melrose. We then consider Hamiltonians H which are `short-range' self-adjoint perturbations of the Laplacian of g. Melrose and Zworski have given a detailed desc…
We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes over the data. We show that optimal generalization error bounds c…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autoco…
Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distri…