New summary measures reveal geometric structure in weighted measures on manifolds.
problem Lack of geometric information in standard weight-only summaries.
method Heat-kernel entropy profiles, tracking nonuniformity across scales.
result Geometric effective sample size discounts nearby or duplicate particles.
We introduce the anti-profile Support Vector Machine (apSVM) as a novel algorithm to address the anomaly classification problem, an extension of anomaly detection where the goal is to distinguish data samples from a number of anomalous and heterogeneous classes based on their pattern of deviation from a normal stable c…
Paper develops a method to predict cancer patient survival using molecular profiles.
problem Accurately predicting cancer patient survival with complex survival-molecular profile relationships.
method Kernel Cox partially linear regression with a novel regularized garrotized kernel machine (RegGKM) method.
result The proposed method outperforms other methods in predicting survival accuracy.
Sharp Gaussian isoperimetry proven along Ricci flow.
problem Proving sharp Gaussian isoperimetric inequality for Ricci flow.
method Using monotonicity formula to prove inequality.
result Exact Gaussian enlargement theorem and concentration estimates.
Unsupervised method selects genes for tumor subtype discovery.
problem High-dimensional tumor gene expression data with noisy variables and heterogeneity.
method Autoencoders for latent space learning, Multiple Kernel Learning for feature selection, clustering.
result Lower redundancy and better clustering performance compared to benchmarks.
A new Mean Shift variant converges after a finite number of iterations for specific kernel shapes.
problem Improving Mean Shift algorithm convergence for specific kernel shapes.
method Developed a novel Mean Shift variant with a triangular kernel profile.
result The new Mean Shift variant converges after a finite number of iterations.
The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.
problem Characterizing generalization properties of high-dimensional kernel ridge regression.
method Bias-variance decomposition of the expected excess risk, considering different regularization schemes and data eigen-profiles.
result The risk curve of kernel regression can be double-descent-like, bell-shaped, or monotonic, depending on n, d, and regularization level.
The study analyzes spectral algorithms for kernel methods and derives generalization error.
problem Estimating generalization error of spectral algorithms for kernel methods.
method Considered spectral algorithms including KRR and GD, derived generalization error as a functional of learning profile.
result Showed the loss localizes on certain spectral scales and conjectured universality of the loss for noisy observations.
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
Study of integral flows on Riemannian manifolds with focus on blow-up profiles and concentration-compactness.
problem Analyzing nonlinear integral flows on Riemannian manifolds with specific focus on blow-up profiles and concentration-compactness.
method Investigation of a family of nonlinear integral flows involving Riesz potentials, focusing on the Hardy-Littlewood-Sobolev (HLS) subcritical and critical regimes.
result Established convergence on unit spheres and certain locally conformally flat manifolds for the dual Yamabe flow.
Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active per…
Kernel testing compares cell states in single-cell data.
problem Comparing non-linear cell states in single-cell data.
method Kernel-based testing framework for non-linear distribution comparison.
result Identifies subtle population variations in cell states.
Framework for continuous-time network data representation learning.
problem Learning reliable representations of dynamic network interactions.
method Three-stage process: intensity estimation, projection learning, evolving node representation construction.
result Trajectories satisfy structural and temporal coherence, providing robust inference.
The paper calculates the number of triangulations and quadrangulations of surfaces based on their profiles.
problem Counting triangulations and quadrangulations of surfaces based on their vertex indices.
method Using a variation of Hodge structure and results from J. Kollár on curvature and Chern classes.
result The number of triangulations and quadrangulations with specific profiles scales with the genus and profile length.
Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However, most of the approaches in the literature assume the in-control population to lie on…
Three RFF-based methods for nonlinear causal discovery in mixed data.
problem Nonlinear causal discovery in mixed data with computational constraints.
method FFML, TRFF, and FFCI methods for score-based, constraint-based, and hybrid causal discovery.
result FFML and TRFF methods provide complementary performance in causal discovery.
Automates GPU kernel optimization for diverse applications.
problem Lack of systematic evaluation for multi-scenario GPU kernel optimization.
method Introduces MSKernelBench and CUDAMaster for automated optimization.
result Significant speedups across various operators, outperforming existing tools.
This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that travelt…
A method selects key genes from tumor transcriptomics data using kernel methods and improves classification performance.
problem Feature selection for tumor classification using gene expression data.
method Multiple Kernel Learning with latent regularization and non-linear dimensionality reduction.
result Improved tumor classification performance on unseen test samples.
Virtual screening (VS) is widely used during computational drug discovery to reduce costs. Chemogenomics-based virtual screening (CGBVS) can be used to predict new compound-protein interactions (CPIs) from known CPI network data using several methods, including machine learning and data mining. Although CGBVS facilitat…
A method to produce personalized classification models to automatically review online dating profiles on Tinder is proposed, based on the user's historical preference. The method takes advantage of a FaceNet facial classification model to extract features which may be related to facial attractiveness. The embeddings fr…
Profile entropy measures learnability and compressibility of discrete distributions.
problem Understanding the learnability and compressibility of discrete distributions.
method Investigates profile entropy, showing its role in estimation, inference, and compression.
result Profile entropy is a fundamental measure unifying estimation, inference, and compression.
A method to describe Riemann surfaces using graph profiles is proposed.
problem Describing Riemann surfaces in a graph-theoretic framework.
method Graph profiles to represent Riemann surfaces, establishing necessary and sufficient conditions for their existence.
result A criterion for the existence of Riemann surfaces with a given signature.
In cheminformatics, compound-target binding profiles has been a main source of data for research. For data repositories that only provide positive profiles, a popular assumption is that unreported profiles are all negative. In this paper, we caution audience not to take this assumption for granted, and present empirica…
Method controls extrapolation in prediction profiles for statistical and machine learning models.
problem Avoiding invalid predictions due to extrapolation in prediction profiles.
method Genetic algorithm optimization over constrained factor regions.
result Optimal factor settings without constraint are often invalid and extrapolated.
Background: While machine learning (ML) models are rapidly emerging as promising screening tools in critical care medicine, the identification of homogeneous subphenotypes within populations with heterogeneous conditions such as pediatric sepsis may facilitate attainment of high-predictive performance of these prognost…
Transient market impact explained via Nash equilibrium in a game.
problem Understanding the transient nature of market impact.
method Analyzing a game between a trader and an arbitrageur, deriving decay kernels.
result Implied transient impact can be derived from trader behavior at Nash equilibrium.
We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new result…
We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincaré profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Timár. In this paper we focus on properties of the Poincaré profiles of groups with …
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.
problem Detecting shape shifts in functional profiles.
method Combining Fréchet mean and shape invariant model for interpretable parameterization of profile deviations.
result Potential shifts in shape deformation process distinguished by significant shifts in amplitude and/or phase.
Study compares isoperimetric profiles on manifolds with integral Ricci curvature bounds.
problem Comparing isoperimetric profiles on manifolds with integral Ricci curvature bounds.
method Extending previous work, the study uses integral bounds on Ricci curvature to prove comparison results for isoperimetric profile functions.
result Comparison results for the Isoperimetric profile function in manifolds with integral bounds on Ricci curvature.
This paper presents a convolutional neural network (CNN) which can be used for forecasting electricity load profiles 36 hours into the future. In contrast to well established CNN architectures, the input data is one-dimensional. A parameter scanning of network parameters is conducted in order to gain information about …
There has been a rapid proliferation of machine learning/deep learning (ML) models and wide adoption of them in many application domains. This has made profiling and characterization of ML model performance an increasingly pressing task for both hardware designers and system providers, as they would like to offer the b…
Estimates lower bounds for isoperimetric profiles and improves on previous estimates for specific manifolds.
problem Estimating lower bounds for isoperimetric profiles of specific Riemannian manifolds.
method Explicit lower bounds for isoperimetric profiles of Riemannian product manifolds.
result Improved lower bounds for isoperimetric profiles and Yamabe constants.
In the context of sub-Riemannian Heisenberg groups Hn, n \geq 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curvature, very similar to ellipsoids. Our main goal is to study the stability of Isoperimetric Profiles.
Paper describes profiles of multivariate normal distributions and novel estimators for mutual information.
problem Estimating mutual information for complex distributions.
method Analytical description of profiles, introduction of Bend and Mix Models, Monte Carlo estimation.
result Bend and Mix Models accurately estimate mutual information profiles and provide Bayesian estimates.
Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…
Random layer-wise pruning profiles are as effective as metric-based ones for various datasets.
problem Reduction of model size and computational resources in neural networks.
method Conducted baseline experiments, developed RL-based search algorithm for finding transferable layer-wise pruning profiles.
result RL-based layer-wise pruning profiles are as good or better than best profiles found on the original dataset via exhaustive search.
Study lampshuffler groups' isoperimetric profiles, refining previous estimates.
problem Relate isoperimetric profiles of lampshuffler groups to their base groups.
method Use lamplighter subgraphs and halo products to find optimal upper bounds.
result Sharp estimates for exponential growth groups, including Brieussel-Zheng groups.
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computa…
The study analyzes how large language models form and express investor risk profiles.
problem Understanding how large language models (LLMs) form and express investor risk profiles.
method Examined three LLMs (GPT, Gemini, and Llama) and assessed their responses to a standardized risk questionnaire under varying prompts.
result LLMs generally form long-term investment profiles, but they exhibit different risk tolerance levels.
Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.
problem Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.
method Normalized Ricci flow on compact surfaces.
result Uniform Lipschitz continuity of isoperimetric profiles under normalized Ricci flow.
A new framework for adaptive behavior using reusable value profiles.
problem Adaptive behavior in changing environments requires switching among value-control regimes, but maintaining separate parameters for each situation is impractical.
method Introduces value profiles: reusable bundles of parameters assigned to hidden states, allowing for state-conditional strategy recruitment without independent parameters for each context.
result Profile-based models outperform simpler alternatives in probabilistic reversal learning, suggesting belief-dependent control of adaptive behavior.
It is shown that, in dimensions <8, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
The hypercube's perimeter is significantly larger than expected near half volume.
problem Understanding the isoperimetric profile of the hypercube.
method Analytical proof of perimeter bounds and comparison to Gaussian isoperimetric profile.
result The isoperimetric profile of the hypercube does not converge to the Gaussian profile as dimension increases.
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion…