arXiv research

Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.

We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.

QR-MIX models joint state-action values as a distribution to handle randomness in MARL.

ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.

In this note we prove that QR-submanifolds of the hyper-Kahler manifolds under some conditions admit the $G_2$ holonomy. We give simplest examples of such QR-submanifolds namely tori. We conjecture that all $G_2$ holonomy manifolds arise in this way.

Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of h…

Spectral method for joint community detection and group synchronization.

New algorithm reduces matrix multiplication time for sparse matrices.

In this paper we study 3-submersions from a QR-hypersurface of a quaternionic Kaehler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kaehler manifolds which are not locally hyper-Kaehler.

This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the naïve divide-and-conquer approach, which splits data into batches of size $m$, computes the l…

In distributional reinforcement learning (RL), the estimated distribution of value function models both the parametric and intrinsic uncertainties. We propose a novel and efficient exploration method for deep RL that has two components. The first is a decaying schedule to suppress the intrinsic uncertainty. The second …

NS-RGS improves orthogonal group synchronization with faster convergence.

The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in information geometry---the differential geometric approach to statistics. The Rieman…

Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincaré duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a simplicial poset the average Euler characteristic of the associated discr…

This work connects Cramér distance to QR-DQN for DRL.

EX-DRL improves extreme quantile prediction for financial risk management.

Proposes a deep learning method to ensure non-crossing quantiles in conditional distributions.

QR-learner estimates individual treatment effects using external data.

We describe an effective method for simultaneously computing of $d$-invariants of infinite families of Brieskorn spheres $Σ(p,q,r)$ with $pq+pr-qr=1$.

TCP provides well-calibrated prediction intervals for nonstationary time series.

Hutch++ optimizes trace estimation for generative models, reducing variance and improving quality.

New method for valid prediction sets in high-dimensional covariate shifts.

New method differentiates square-root Kalman filters robustly.

We propose an algorithm for electrocardiogram (ECG) segmentation using a UNet-like full-convolutional neural network. The algorithm receives an arbitrary sampling rate ECG signal as an input, and gives a list of onsets and offsets of P and T waves and QRS complexes as output. Our method of segmentation differs from oth…

Optimal inference in distributed quantile regression without stringent scaling conditions.

Revisits PCA with new formulations and insights.

The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality approximations, the number of landmark points is chosen to be greater than the target rank. Ho…

Study uses APT and QR to identify risk factors affecting crude oil returns.

We shed new insights on the two commonly used updates for the online $k$-PCA problem, namely, Krasulina's and Oja's updates. We show that Krasulina's update corresponds to a projected gradient descent step on the Stiefel manifold of the orthonormal $k$-frames, while Oja's update amounts to a gradient descent step using…

This work extends VQR to non-linear cases and provides scalable solvers.

Learning an effective representation for high-dimensional data is a challenging problem in reinforcement learning (RL). Deep reinforcement learning (DRL) such as Deep Q networks (DQN) achieves remarkable success in computer games by learning deeply encoded representation from convolution networks. In this paper, we pro…

Develops new algorithms for QRF to handle mixed-frequency and longitudinal data.

Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (…

Improved tensor GLM estimation for complex data.

Paper tackles joint community detection and phase synchronization in stochastic block models.

The paper studies topological and dynamic properties of boundaries in geometric group actions.

AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.

We showcase how Quantile Regression (QR) can be applied to forecast financial returns using Limit Order Books (LOBs), the canonical data source of high-frequency financial time-series. We develop a deep learning architecture that simultaneously models the return quantiles for both buy and sell positions. We test our mo…

Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have infinite dimensions and are highly correlated. An essential issue for classifying dyn…

The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. With the aid of these subspace projections, a fast deflation meth…

Paper proposes a deep learning model for real-time ECG signal segmentation.

New algorithms improve uncertainty estimation in satellite precipitation predictions.

Neural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating its flip points. A flip point is any point that lies on the boundary between two o…

New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.

In this article, we prove that the equation of the Schrödinger maps from ${\bf R}^2$ to the hyperbolic 2-space ${\bf H}^2$ is SU(1,1)-gauge equivalent to the following 1+2 dimensional nonlinear Schrödinger-type system of unknown three complex functions $p,q,r$ and a real function $u$: {c} iq_t+q_{z{\bar z}}-2u q+2({\ba…

Audit shows risk claims from distributional reinforcement learning agents are often false.

We study geodesic equations for a family of right-invariant Riemannian metrics on the group of diffeomorphisms of a compact manifold. The metrics descend to Fisher's information metric on the space of smooth probability densities. The right reduced geodesic equations are higher-dimensional generalisations of the $μ$--H…

A new retraction on Stiefel manifold with a closed-form inverse.