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.
Magnitude of Euclidean domains predicts Willmore energy in odd dimensions.
This paper proposes an approach to the joint modeling of the short-time Fourier transform magnitude and phase spectrograms with a deep generative model. We assume that the magnitude follows a Gaussian distribution and the phase follows a von Mises distribution. To improve the consistency of the phase values in the time…
In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing w…
New measures quantify diversity of latent representations using metric space magnitude.
Accelerated magnetic resonance (MR) scan acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts …
Improves functional linear regression with shape transfer learning.
We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an integral exists then the boundary curve of the domain determines an algebraic curve in…
Neural model outperforms ETAS in forecasting Central Apennines earthquakes.
Most learning algorithms are not invariant to the scale of the function that is being approximated. We propose to adaptively normalize the targets used in learning. This is useful in value-based reinforcement learning, where the magnitude of appropriate value approximations can change over time when we update the polic…
Novel unsupervised scheme for highly imbalanced and overlapping datasets.
Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the training data are obtained using traditional PDE solvers. Thereby, the uses of deep-le…
Nowadays, users open multiple accounts on social media platforms and e-commerce sites, expressing their personal preferences on different domains. However, users' behaviors change across domains, depending on the content that users interact with, such as movies, music, clothing and retail products. In this paper, we pr…
We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Ou…
Efficient audio synthesis is an inherently difficult machine learning task, as human perception is sensitive to both global structure and fine-scale waveform coherence. Autoregressive models, such as WaveNet, model local structure at the expense of global latent structure and slow iterative sampling, while Generative A…
Estimates changes in parameters from sparse binomial observations.
Generative model learns shape drift for quantifying domain uncertainty in hemodynamics.
A fast deep learning method for parallel MRI without calibration.
Magnitude homology reveals that graphs can have torsion subgroups.
Analyze SGD with biased gradients, improving convergence rates and accuracy.
We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural approach to this task, accompanied by a thorough experimental evaluation on a publicly …
Defines magnitude for length spaces with measures, agreeing with finite spaces' magnitude.
SGPT-PINNs solve PDEs with sparse, small models.
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…
Characterizes Anosov reducible representations in terms of eigenvalues.
This research quantifies neural networks using magnitude, a topological invariant.
Magnitude of manifolds linked to Riesz energies and beta functions.
Lookahead pruning extends single-layer optimization to multi-layer, outperforming magnitude-based pruning.
Magnitude is not continuous but may be stable for most finite metric spaces.
Are expansions and recessions more likely to end as their magnitude increases? In this paper we apply parametric hazard models to investigate this issue in a sample of 16 countries from 1881 to 2000. For the total sample we find evidence of positive magnitude dependence for recessions, while for expansions we are not a…
Magnitude study on manifolds using fractional Laplacian.
Deep reinforcement learning (DRL) is capable of learning high-performing policies on a variety of complex high-dimensional tasks, ranging from video games to robotic manipulation. However, standard DRL methods often suffer from poor sample efficiency, partially because they aim to be entirely problem-agnostic. In this …
Hepworth, Willerton, Leinster and Shulman introduced the magnitude homology groups for enriched categories, in particular, for metric spaces. The purpose of this paper is to describe the magnitude homology group of a metric space in terms of order complexes of posets. In a metric space, an interval (the set of points b…
Magnitude of geometric shapes studied for smooth manifolds, revealing spectral geometry insights.
This paper introduces new invariants for time series analysis.
A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.
ProtoTransfer learns from unlabeled data to classify unseen tasks.
Magnitude is a real-valued invariant of metric spaces, analogous to the Euler characteristic of topological spaces and the cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies the analogies between various cardinality-like invariants in mathematics. Altho…
Causal invariance can improve finite-sample domain adaptation, but only when the target risk margins are large.
Novel metric space magnitude and weighting vectors improve machine learning tasks.
Non-invasive myoelectric prostheses require a long training time to obtain satisfactory control dexterity. These training times could possibly be reduced by leveraging over training efforts by previous subjects. So-called domain adaptation algorithms formalize this strategy and have indeed been shown to significantly r…
REx tackles distributional shift by reducing risk differences across domains.
I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…
Given two candidate models, and a set of target observations, we address the problem of measuring the relative goodness of fit of the two models. We propose two new statistical tests which are nonparametric, computationally efficient (runtime complexity is linear in the sample size), and interpretable. As a unique adva…
Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, , can be detected and quantified by studying the correlations in the magnitude series , i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact …
Magnitude-based features capture interactions between different entities in multispecies spatial data.
A new pruning criterion reduces model size and improves performance.
Graphs models are vulnerable to distribution shifts, which this work explains and mitigates.
EQShapelets detect earthquakes with high accuracy and interpretability.