Spherical Principal Curvesstat.ME
New approach for principal curves on spherical data.
problem Dimension reduction of spherical data.
method Projection of data onto a continuous curve on a sphere.
result Stationary principal curves on a sphere.
On-device research index
arXiv research
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.
168,695 papers · 148 categories
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48 results for “curve data”
We use learning curves to analyze deep networks and evaluate model design.
problem Evaluate design choices in deep networks.
method Propose a method to robustly estimate learning curves, abstract their parameters, and evaluate different parameterizations.
result Interesting observations on the effectiveness of different parameterizations.
Transforms curves and surfaces for efficient geometric analysis.
problem Efficiently analyzing and comparing curves and surfaces.
method Square root velocity transformation for curves and intrinsic comparison for surfaces.
result Fundamental geometric properties of curves under the transformation.
Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes have been successfully applied to model functional data in a variety of application…
A new metric-based principal curve method learns 1D manifolds from spatial data.
problem Learning 1D manifolds from spatial data.
method Metric-based Principal Curve (MPC) approach.
result The method effectively learns the shape of 1D manifolds from synthetic and real datasets.
Extends curve theory to non-smooth data with finite curvature and torsion.
problem Applying classical curve theory to non-smooth data.
method Using distributional derivative measures of functions of bounded variation.
result Essentially unique non-smooth curve solution with finite total curvature and torsion.
Paper benchmarks machine learning for detecting process curve drifts.
problem Detecting drifts in multivariate manufacturing process data.
method Synthetic data generation and evaluation score introduction.
result Existing algorithms often fail with complex drift scenarios.
A Survey of Learning Curves with Bad Behavior: or How More Data Need Not Lead to Better Performancecs.LG
Learning curves show more data doesn't always improve performance.
problem The surprising finding that more data doesn't always lead to better generalization performance.
method A survey of learning curves, focusing on those that indicate more data doesn't necessarily improve performance.
result Learning curves can show that more data doesn't always lead to better generalization performance.
Study ranks of elliptic curves via prime averages.
problem Classifying elliptic curves by rank.
method Average Frobenius trace over primes, data science experiments.
result Oscillating pattern in average trace values, correlates with rank.
3D filament plots visualize curves in datasets, avoiding visual clutter.
problem Visualizing high-dimensional data relationships in scatterplots of points.
method Construct 3D filament plots using linear isometries and Frenet-Serret systems.
result 3D filament plots preserve Euclidean distances and avoid visual clutter.
Constructs universal local deformations for curves and differential forms.
problem Local deformations of curves and differential forms under preservation of periods.
method Develops Kuranishi families for pairs of curves and meromorphic 1-forms, focusing on hyperelliptic cases.
result First paper in a series developing a deformation theory for spectral curve data of integrable systems.
On Charge-3 Cyclic Monopolesmath-ph
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of g…
The delta invariant of curves on rational surfaces II: Poincaré series and topological aspectsmath.GT
Study delta invariant of curves on rational surfaces using topological methods.
problem Calculate delta invariant for curves embedded in rational singularities.
method Use topological techniques and Poincaré series.
result Develop formulae for delta invariant in terms of embedded data.
When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. Principal curves act as a nonlinear generalization of PCA and the present paper proposes a novel algorithm to automatically and sequentially learn principal curves from d…
This paper uses crypto derivatives data to estimate yield curves for cryptocurrencies.
problem Estimating yield curves for cryptocurrencies without bond markets.
method Using mathematical tools and data from cryptocurrency derivatives markets.
result Yield curves can be constructed for cryptocurrencies using derivative data.
A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model parameters are estimated in a maximum likelihood framework through a dedicated Expectat…
This paper introduces a novel monotone curve estimation framework based on convex duality.
problem Estimating smooth, continuous, and monotonic curves in data.
method Convex duality and optimal transport theories.
result Established statistical guarantees for monotone curve estimates.
The paper shows how the generalization curve can have multiple peaks, influenced by data and learning algorithm biases.
problem Understanding the generalization behavior of linear regression models under varying parameterizations.
method Analyzes generalization loss in linear regression models with varying parameterizations, both under- and over-parameterized.
result The generalization curve can have an arbitrary number of peaks, and their locations can be controlled.
The paper proves -convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves -convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional.
result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regres…
Statistical approaches for Functional Data Analysis concern the paradigm for which the individuals are functions or curves rather than finite dimensional vectors. In this paper, we particularly focus on the modeling and the classification of functional data which are temporal curves presenting regime changes over time.…
Applications of Machine Learning in Pharmacogenomics: Clustering Plasma Concentration-Time Curvesstat.AP
The paper clusters PK curves using ML, finding it useful for identifying similar patterns.
problem Improving drug development and patient outcomes through ML in pharmacogenomics.
method Unsupervised clustering of PK curves using various dissimilarity measures.
result Euclidean distance is most suitable for clustering PK curves, and clustering can validate pharmacogenomic results.
In this paper we introduce a geometric quantity, the -multiplicity, that controls the length of a smooth curve as it evolves by curve shortening flow. The length estimates we obtain are used to prove results about the level set flow in the plane. If is locally-connected, connected and compact, then the level set…
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curve…
Nelson and Siegel curves are widely used to fit the observed term structure of interest rates in a particular date. By the other hand, several interest rate models have been developed such their initial forward rate curve can be adjusted to any observed data, as the Ho-Lee and the Hull and White one factor models. In t…
A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curvemath.NA
We derive a variational model to fit a composite Bézier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second o…
The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.
problem Understanding surfaces with spherical curvature lines and their generation mechanisms.
method The approach involves Lie sphere transformations, Legendre curves, and polynomial conserved quantities of connections.
result Lie applicable surfaces with exactly one family of spherical curvature lines are generated by the lift of constrained elastic curves.
Learn2Evaluate uses learning curves to estimate high-dimensional prediction performance.
problem Estimating test performance in high-dimensional data settings is challenging.
method Learn2Evaluate uses learning curves to estimate test performance at the total sample size.
result Learn2Evaluate provides a lower confidence bound for performance estimation.
Subgroup detection in linear growth curve models with generalized linear mixed model (GLMM) treesstat.ME
GLMM trees identify subgroups with different growth patterns in longitudinal data.
problem Identifying subgroups with distinct growth trajectories in longitudinal studies.
method Extended GLMM trees for longitudinal data.
result Extended GLMM trees outperform other methods in accuracy and speed.
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
Paper details Hilbert-curve for high-performance data mining.
problem Efficiently mapping multi-dimensional data to one dimension.
method Defines Hilbert-curve using finite automaton and context-free grammar.
result Cache-oblivious algorithms for matrix operations and clustering.
We give a simple characterization of the parabolic geodesics introduced by Cap, Slovak and Zadnik for all parabolic geometries. This goes through the definition of a natural connection on the space of Weyl structures. We then show that parabolic geodesics can be characterized as the following data: a curve on the manif…
Functional Mixture Discriminant Analysis with hidden process regression for curve classificationstat.ME
We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves presenting regime changes. The model parameters are learned by maximizing the observed-da…
Proposes MCC-F1 curve for better binary classification evaluation.
problem Misleading performance evaluations with ROC and PR curves for imbalanced data.
method Introduces MCC-F1 curve combining MCC and F1 score.
result MCC-F1 curve provides clearer classifier differentiation.
Scheme minimizes -elastic energy of curves over time.
problem Minimizing -elastic energy of curves over time.
method Minimizing movement scheme with approximate normal graphs.
result Short-time existence and lower bound on solution's lifetime.
Light curve completion and forecasting using fast and scalable Gaussian processes (MuyGPs)astro-ph.IM
Predict missing and future data points in light curves using scalable Gaussian Processes.
problem Gappy time-series data from commercial cameras confound light curve prediction.
method MuyGPs, a scalable framework for hyperparameter estimation of Gaussian Processes using nearest neighbors sparsification and local cross-validation.
result MuyGPs enable accurate prediction of missing and future data points in light curves.
Log-Aesthetic Curves: Similarity Geometry, Integrable Discretization and Variational Principlesnlin.SI
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize them as invariant curves under the integrable flow on plane curves which is gov…
Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congea…
Slice Tuner: A Selective Data Acquisition Framework for Accurate and Fair Machine Learning Modelscs.LG
Slice Tuner optimizes data acquisition for accurate and fair machine learning models.
problem Acquiring enough data for all slices of data to ensure accurate and fair models.
method Selective data acquisition using convex optimization and iterative learning curve updates.
result Significantly outperforms baselines in model accuracy and fairness.
Study on Brownian motion on discrete curve spaces, proving stochastic completeness.
problem Analyzing Brownian motion on spaces of discrete curves.
method Introduced and studied Brownian motion on spaces of discrete regular curves with Sobolev-type metrics.
result All geodesically complete spaces of discrete regular curves are stochastically complete.
LC-PFN predicts learning curve performance more accurately and faster than MCMC.
problem Bayesian extrapolation of learning curves is computationally expensive and overly restrictive.
method Prior-Data Fitted Neural Networks (PFNs) for approximate Bayesian inference.
result LC-PFN outperforms MCMC in accuracy and is significantly faster.
Flow deforms curves to match an embedded target.
problem Evolve curves to match an embedded target curve.
method Target flow with curve shortening and forcing term.
result Smooth convergence to the target curve.
Curve shortening flow's regularity depends on initial conditions after a certain time.
problem Understanding the regularity of evolving curves under curve shortening flow.
method Proposing and proving principles of controllable regularity based on initial conditions.
result No regularity estimate holds before a specific time, .
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
Deep networks can classify data on smooth curves with high probability.
problem Classifying data from two disjoint smooth curves on the unit sphere.
method Gradient descent on a deep neural network, proving convergence and generalization via NTK dynamics.
result Randomly-initialized gradient descent learns to classify all points on the two curves with high probability when the network is sufficiently deep.
The paper studies how curves evolve under area constraints and converges to a critical point.
problem Evolution of plane curves with fixed area under elastic energy gradient.
method Local and global existence of the flow, simplicity assumption, Łojasiewicz--Simon inequality.
result The evolving curve's length remains bounded and converges to a critical point.
Bayesian method models multivalued power data from wind farms.
problem Accurate modeling of power curves with multivalued relationships.
method Overlapping mixture of probabilistic regression models.
result Model accurately represents practical power data.
We construct a sequence of commuting central affine curve flows on invariant under the action of and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve flow is a solution of the j-th flow of Gelfand-Dickey (GD) hierarchy on the s…