arXiv research

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

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 …

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.

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

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

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…

Revisits PCA with new formulations and insights.

A deep learning algorithm for ECG segmentation.

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

Spectral method for joint community detection and group synchronization.

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

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…

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

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

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

QR-learner estimates individual treatment effects using external data.

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

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

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.

Optimal inference in distributed quantile regression without stringent scaling conditions.

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 (…

New algorithm reduces matrix multiplication time for sparse matrices.

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

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

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…

New algorithms improve uncertainty estimation in satellite precipitation predictions.

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

In traditional reinforcement learning, an agent maximizes the reward collected during its interaction with the environment by approximating the optimal policy through the estimation of value functions. Typically, given a state s and action a, the corresponding value is the expected discounted sum of rewards. The optima…

NS-RGS improves orthogonal group synchronization with faster convergence.

Distributional Reinforcement Learning (RL) differs from traditional RL in that, rather than the expectation of total returns, it estimates distributions and has achieved state-of-the-art performance on Atari Games. The key challenge in practical distributional RL algorithms lies in how to parameterize estimated distrib…

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

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning…

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…

Recurrent neural networks (RNN) have been successfully applied to various sequential decision-making tasks, natural language processing applications, and time-series predictions. Such networks are usually trained through back-propagation through time (BPTT) which is prohibitively expensive, especially when the length o…

This paper investigates Shampoo's heuristics and decouples preconditioner updates.

Toda flow explained as a porous medium equation.

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…

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…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-conve…

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…

Improved tensor GLM estimation for complex data.