Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning algorithms. However, there still lacks a principled method for learning the metric scali…
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “base metrics”
We propose a new metric to measure domain divergence and a new domain adaptation method for time-series classification. The metric belongs to the class of probability distributions-based metrics, is transductive, and does not assume the presence of source data samples. The 2-stage method utilizes an improved autoregres…
Defines a new Randers metric based on an existing one.
problem No specific problem stated; focuses on defining a new metric.
method Defines a new left-invariant Randers metric based on an existing one .
result Shows that is of Berwald (Douglas) type if and only if is of Berwald (Douglas) type.
Few-shot learning aims to learn classifiers for new classes with only a few training examples per class. Most existing few-shot learning approaches belong to either metric-based meta-learning or optimization-based meta-learning category, both of which have achieved successes in the simplified "-shot -way" image c…
Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to maintain the basic properties of such metrics, e.g., non-negative, identity of i…
A simpler metric for latent space geometry.
problem Complexity in capturing geometric structure of data manifolds.
method Prior-based approximate latent Riemannian metric.
result The proposed metric is simple, efficient, and robust.
Study creates web interface to elicit user-preferred metrics.
problem Eliciting classification metrics that align with user preferences.
method Developed a web-based interface and conducted a user study.
result Users preferred metrics that align with their task and context.
Study evaluates relevance metrics for similarity-based model explanations.
problem Providing understandable explanations for complex model predictions.
method Evaluated three relevance metrics using three tests.
result Cosine similarity of gradients performs best for explanations.
New Fourier metrics equivalent to Wasserstein distances in image processing.
problem Equivalence of Fourier-based and Wasserstein metrics in imaging problems.
method Extensions of Fourier-based metrics to handle different centers of mass and discrete measures, showing equivalence to Wasserstein distances.
result New Fourier metrics are equivalent to Wasserstein distances with explicit constants, improving runtime in image processing.
Natural metrics provide a way to induce a metric on the tangent bundle from the metric on its base manifold. The most studied type is the Sasaki metric, which applies the base metric separately to the vertical and horizontal components. We study a more general class of metrics which introduces interactions between the …
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.
ID-ExpO fine-tunes neural networks for more faithful explanations.
problem Improving the faithfulness of explanations for complex machine learning models.
method Differentiable insertion/deletion metric-aware regularizers for optimization.
result Fine-tuned predictors produce more faithful explanations.
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…
A new DR formulation improves metric learning for faster and more stable performance.
problem Learning embeddings for class separation in metric learning.
method Distance-ratio (DR) formulation for metric learning.
result DR formulation achieves improved or comparable generalization performances.
Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general met…
New method uses interval-based metric to validate prediction uncertainty in machine learning.
problem Validation of prediction uncertainty in machine learning regression tasks is unreliable due to heavy-tailed distributions.
method Shift from variance-based metrics to interval-based Prediction Interval Coverage Probability (PICP).
result PICP method more quickly and reliably tests prediction intervals than variance-based metrics.
New metric learning approach for tree data reduces computation cost.
problem Efficiently computing distances between ordered labeled trees.
method Introduced pq-grams and a differentiable weighted pq-gram distance, combined with LMNN for optimization.
result Significantly reduces computation time for tree classification problems.
This paper develops a new method for eliciting more flexible metrics, improving fairness and applicability.
problem Limited flexibility in existing metric elicitation strategies for reflecting user preferences.
method Develops a strategy for eliciting quadratic metrics based on predictive rates, requiring only relative preference feedback.
result Achieves near-optimal query complexity and broadens the use cases for metric elicitation.
New approaches estimate recommendation metrics using sampling.
problem Understanding and resolving the use of sampling for recommendation evaluation.
method MLE and ME principles for empirical rank distribution recovery.
result Advantages of new approaches for top-k metrics estimation.
Few-shot learning has become essential for producing models that generalize from few examples. In this work, we identify that metric scaling and metric task conditioning are important to improve the performance of few-shot algorithms. Our analysis reveals that simple metric scaling completely changes the nature of few-…
Study Fano fibrations and Kähler-Einstein metrics on their bases.
problem Understand geometric structures and metrics on Fano fibrations.
method Construct -forms and solve twisted Kähler-Einstein equations.
result Singular Kähler metrics on Fano fibrations satisfy twisted Kähler-Einstein equations.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
We consider the Kähler-Ricci flow on certain Calabi-Yau fibration, which is a Calabi-Yau fibration with one dimensional base or a product of two Calabi-Yau fibrations with one dimensional bases. Assume the Kähler-Ricci flow on total space admits a uniform lower bound for Ricci curvature, then the flow converges in Grom…
Distance/Similarity learning is a fundamental problem in machine learning. For example, kNN classifier or clustering methods are based on a distance/similarity measure. Metric learning algorithms enhance the efficiency of these methods by learning an optimal distance function from data. Most metric learning methods nee…
Completeness of Riemannian metrics: an application to the control of constrained mechanical systemseess.SY
We improve Riemannian metrics for constrained systems control.
problem Controlling mechanical systems with configuration constraints.
method Constructing complete Riemannian metrics by modifying incomplete ones.
result A controller can be found to satisfy a design criterion.
New definition of naturally reductive Finsler manifolds using geodesic graphs.
problem Defining naturally reductive Finsler manifolds using geodesic graphs.
method Proposed a new geometrical definition using geodesic graphs and constructed examples of Finsler metrics.
result Explicit examples of Finsler naturally reductive metrics constructed.
Study extends continuity equation for Gauduchon metrics.
problem Continuity equation for Gauduchon metrics.
method Solution to Gauduchon conjecture by Székelyhidi, Tosatti, and Weinkove.
result Extended interval of maximal existence for continuity equation.
This paper reviews metrics to assess AI model calibration accuracy.
problem AI model probabilities do not always match their true accuracy.
method Comprehensive review of 82 probability calibration metrics.
result Identified 4 classifier families and 1 object detection family of metrics.
Pseudo-Riemannian Ricci-flat and Flat Warped Geometries and New Coordinates for the Minkowski metricgr-qc
It is well-known that the Einstein condition on warpedgeometries requires the fibres to be necessarily Einstein. However, exact warped solutions have often been obtained using one- and two-dimensional bases. In this paper, keeping the dimensions and signatures of the base and the fibre independently arbitrary, we obtai…
Consider a fibred compact Kähler manifold X endowed with a relatively ample line bundle, such that each fibre admits a constant scalar curvature Kähler metric and has discrete automorphism group. Assuming the base of the fibration admits a twisted extremal metric where the twisting form is a certain Weil-Petersson type…
We present a classification of the complete, simply connected, contact metric -spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx invariant, it turns out that the base is a complexification or a para-complexification of a …
The LoCA Regret: A Consistent Metric to Evaluate Model-Based Behavior in Reinforcement Learningcs.LG
Introduces LoCA regret to evaluate model-based RL methods.
problem Lack of consistent metrics to evaluate model-based RL methods.
method Inspired by neuroscience, introduces LoCA regret to measure model-based behavior.
result LoCA regret can identify model-based behavior and assess how close methods are to optimal model-based behavior.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Extends Kähler metrics theory to symplectic manifolds with toric actions.
problem Extending invariant Kähler metrics theory to symplectic manifolds with toric actions.
method Using Delzant subspaces and Lagrangian fibrations, establishing a correspondence between metrics and connections.
result Characterizes extremal invariant Kähler metrics as those with scalar curvature on base integral affine manifold.
The paper proves compactness of warped product metrics on S²×S¹ with varying base metrics.
problem Proving compactness of warped product metrics on S²×S¹ with nonnegative scalar curvature.
method Using Gromov-Sormani MinA scalar curvature compactness conjecture, the paper proves a uniform diameter bound for the base surfaces, compactness of the base warping functions, and convergence of the metrics.
result The metrics converge to a limit metric with nonnegative scalar curvature in the distributional sense.
Einstein metrics on homogeneous torus bundles
problem Einstein metrics on total space of homogeneous torus bundles
method Descend to common base and establish estimates
result Prove precompactness theorem for Einstein manifolds
Study analyzes neural network models to understand generalization performance.
problem Understanding good generalization in neural networks.
method Analyzed a corpus of models from a public contest, breaking ALPHAHAT into scale and shape metrics.
result Identified a Simpson's paradox in metric performance across different model depths and regularization hyperparameters.
Differentiable optimization bridges arbitrary metrics to tree metrics.
problem Designing algorithms to convert arbitrary metrics to tree metrics with guarantees.
method DeltaZero framework, leveraging differentiable Gromov hyperbolicity.
result DeltaZero consistently achieves state-of-the-art distortion on synthetic and real-world datasets.
In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous -Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a questi…
Compact quasi-Einstein metrics with constant scalar curvature are locally homogeneous in 3D.
problem Characterize compact quasi-Einstein metrics with constant scalar curvature.
method Connection to Sasakian geometry and circle bundles over Einstein metrics.
result Compact quasi-Einstein metrics with constant scalar curvature are locally homogeneous in 3D.
Metric learning makes it plausible to learn distances for complex distributions of data from labeled data. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well. Those that learn multiple metrics throughout the space have demonstrated superi…
This paper focuses on the horse race of weekly idiosyncratic momentum (IMOM) with respect to various idiosyncratic risk metrics. Using the A-share individual stocks in the Chinese market from January 1997 to December 2017, we first evaluate the performance of the weekly momentum based on raw returns and idiosyncratic r…
We study the existence of projectable -invariant Einstein metrics on the total space of -equivariant fibrations , for a compact connected semisimple Lie group . We obtain necessary conditions for the existence of such Einstein metrics in terms of appropriate Casimir operators, which is a generali…
Study local models for special Kähler metrics near discriminant locus components.
problem Analyzing singularities of special Kähler metrics along discriminant locus of Hitchin base.
method Computed Taylor expansion, defined subsystems, and analyzed asymptotics and convergence of metrics.
result Logarithmic asymptotics in transversal directions and convergence to a metric on strata.
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous…
This paper introduces a new financial metric for the art market. The metric is based on the price per unit of area and is applicable to two-dimensional art objects such as paintings.
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…