arXiv research

Optimizes risk measures given known marginal distributions of two unknown factors.

Optimizes graph spectral density learning for large networks.

A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…

This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …

Spectral clustering improves accuracy and efficiency for clustering discrete distributions.

Unified framework for spectral methods, kernel learning, and manifold unfolding.

We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which minimise the second eigenvalue of the graph Laplacian of the projected data, whic…

We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian matrices in terms of the between cluster separation, and within cluster connecti…

We study the asymptotic behavior of the difference $Δρ^{X, Y}_α:= ρ_α(X + Y) - ρ_α(X)$ as $α\rightarrow 1$, where $ρ_α$ is a risk measure equipped with a confidence level parameter $0 < α< 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where …

We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a …

Spectral clustering for directed graphs using likelihood estimation.

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular …

Study shows non-spectrality of certain curves and line segments.

For large genus, spectral gaps on hyperbolic surfaces approach a limit.

Paper finds exact Hessian sharpness in deep matrix factorization.

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…

We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…

In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may …

Paper estimates spectral risk measures for insurance data with truncated and censored data.

Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems…

In this paper, we study the confounder detection problem in the linear model, where the target variable $Y$ is predicted using its $n$ potential causes $X_n=(x_1,...,x_n)^T$. Based on an assumption of rotation invariant generating process of the model, recent study shows that the spectral measure induced by the regress…

A new measure quantifies how risk-averse different risk measures are.

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…

Estimates spectral risk measures from i.i.d. samples.

Study shows links with unbounded annular Khovanov gradings but bounded Floer gradings.

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…

This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on …

Study minimizes risk in MDPs with spectral measures.

Spectral clustering identifies clusters of multivariate extremes.

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and eff…

Optimizes two-sample tests for non-Euclidean domains using spectral regularization.

Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.

Study spectral distances on compact RCD spaces.

Spectral ranking methods are improved against semi-random graph sampling.

Study of asymmetric rank-one tensor models with non-Gaussian noise.

New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model…

Spectral analysis detects structural changes in financial networks.

Proposes a Gaussian process for graph signals using adaptive spectral kernels.

The paper defines surface area for graphs and derives spectral estimates.

Paper quantifies uncertainty in pairwise comparison models.

Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.

A new topology improves decentralized learning efficiency and accuracy.

Proposes a new framework for risk-sensitive RL using deep nets.

Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be clustered. One of the central pieces of spectral clustering is the construction of an…

A new method for risk-sensitive reinforcement learning using Spectral Risk Measures.

Paper provides robustness bounds for GNNs against adversarial attacks.