The Minimal Learning Machine improves regression performance with reference point selection.
problem Improving the performance of the Minimal Learning Machine (MLM) in regression tasks.
method Developed theoretical guarantees for MLM's interpolation and approximation capabilities. Proposed clustering-based methods for selecting reference points to enhance MLM's generalization.
result Clustering-based methods for reference point selection outperform random selection, especially with a small number of points.
Method learns neural network to overestimate reference function with guarantees.
problem Learning a neural network to overestimate a reference function on a given domain.
method Two-step process: constructing Majoring Points and optimizing a neural network.
result The learned neural network overestimates the reference function on the domain.
Study measures gender bias in machine translation using multiple reference points.
problem Measuring and identifying gender bias in machine translation.
method Used an optimal non-biased translator, reference points from occupational statistics and survey.
result Found bias against both genders, but more against women, and found occupations have a greater effect than adjectives.
New method learns cell trajectories from multiple snapshots.
problem Inferring cell trajectories from limited, single-time-point data.
method Multi-marginal Schrödinger Bridges with iterative reference refinement.
result Effective in capturing long-term dependencies and learning from multiple time points.
Modeling consumption and investment decisions with reference point and drawdown constraints.
problem Modeling consumption and investment decisions with reference point and drawdown constraints.
method Solving a stochastic control problem to derive value function, optimal consumption plan, and investment strategy in semi-explicit forms.
result Five important thresholds of wealth, all as functions of h, and significant economic implications. In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from those points to the rest of the data, as well as how at the weights on the refere…
This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment from the realisation. The choice of over-optimism or over…
Study shows mutual funds add little value for uninformed investors.
problem Understanding the performance of actively managed equity mutual funds for uninformed investors.
method Constructed a reference portfolio using prices and supply information, analyzed various subsets of funds, and compared to market index.
result Mutual funds provide insignificant alpha for uninformed investors, with negative and significant alpha when compared to the market index.
We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagati…
New method detects if data points were used in training models with low cost and high power.
problem Detecting if a particular data point was used in training a model.
method Fine-grained modeling of null hypothesis in likelihood ratio tests, leveraging reference models and population data.
result RMIA has superior test power compared to prior methods, even at extremely low false positive rates.
We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the moduli space of semistable oriented torsion free sheaves and the quot scheme assoc…
Motivated by the application to spacetimes of general relativity we investigate the geometry and regularity of Lorentzian manifolds under certain curvature and volume bounds. We establish several injectivity radius estimates at a point or on the past null cone of a point. Our estimates are entirely local and geometric,…
New method assesses prediction intervals across different operating points.
problem Difficulty in comparing prediction intervals across studies.
method Operating characteristics curves and gain over a simple reference.
result A novel operating point agnostic assessment methodology for prediction intervals.
Optimal order execution strategies for brokers under reference benchmarks.
problem Maximizing broker's utility of excess profit-and-loss subject to reference strategies.
method Formulated as a utility maximization problem, optimal strategies derived in closed form.
result General reference strategies can be approximated by piece-wise linear combinations of IS and TC orders.
ASK-NN detects distribution drifts in LLM-generated text.
problem Hallucinations and artificial text in LLM-generated outputs.
method Asymmetric two-sample test based on directed k-nearest-neighbor graph.
result ASK-NN is competitive with baselines on various benchmarks.
In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.
KCUSUM detects abrupt changes in real-time data streams efficiently.
problem Detecting abrupt changes in high-volume scientific data streams.
method Kernel-based Cumulative Sum (KCUSUM) algorithm using Maximum Mean Discrepancy (MMD).
result KCUSUM outperforms traditional CUSUM in online change point detection.
The study defines and characterizes extrinsic catenaries in hyperbolic space.
problem Understanding catenaries in hyperbolic geometry.
method Defined extrinsic catenaries in hyperbolic plane, characterized them, and proved their relation to minimal surfaces.
result Extrinsic catenaries in hyperbolic space are critical points of a potential functional and generating curves of minimal surfaces.
Survey on finite group actions on manifolds.
problem Understanding actions of finite groups on manifolds.
method Analyzes the restriction of actions to subgroups and considers group and manifold properties.
result Provides information on subgroup actions and their properties.
We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.
Model shows how heterogeneity in strategies and risk tolerance affects financial market stability.
problem Understanding how heterogeneity impacts financial market dynamics.
method Agent-based model incorporating heterogeneous investment strategies and risk tolerance.
result Heterogeneity in strategies and risk tolerance suppresses price fluctuations.
We introduce a weak notion of barycenter of a probability measure μ on a metric measure space (X,d,m), with the metric d and reference measure m. Under the assumption that optimal transport plans are given by mappings, we prove that our barycenter B(μ) is well defined; it is a probability measur…
Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only while training, but also when deployed at scales ranging from data centers all th…
The paper analyzes how conformal prediction works with contaminated reference data.
problem The impact of contamination on the validity and power of conformal prediction methods.
method The paper analyzes the impact of contamination on the validity of conformal methods and proposes a data-cleaning framework to enhance power.
result The proposed data-cleaning framework can effectively enhance power while maintaining type-I error control.
Study replicates reference-dependent preferences impact on risk-return trade-off in Chinese stock market.
problem Impact of reference-dependent preferences on risk-return trade-off in Chinese stock market.
method Utilized CGO proxy, econometric techniques (Dependent Double Sorting, Fama-MacBeth regressions), and data from 1995-2024.
result Reference-dependent preferences have a weaker or absent positive risk-return relationship in the Chinese market.
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D2, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the Conley index theory of discrete braid classes as introduced in [Ghrist et al., C. …
For simply connected compact exceptional Lie groups G=F4,E6 and E7, we consider two involutions σ,γ and determine the group structure of subgroups Gσ,γ of G which are the intersection Gσ∩Gγ of the fixed points subgroups of Gσ and Gγ. The motivation is as follows. In [1](see the Referen…
We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or co…
We study finite-sum nonconvex optimization problems, where the objective function is an average of n nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference …
Catenaries defined on any Riemannian surface using intrinsic distance.
problem Defining catenaries on Riemannian surfaces.
method Defining catenaries as critical points of a potential functional, calculating potential with intrinsic distance, and characterizing using curvature.
result Characterization of catenaries on various Riemannian surfaces.
GRPO optimizes LLMs with verifiable rewards, amplifying policy success.
problem Improving LLMs' reasoning under verifiable binary rewards.
method Introduces GRPO, analyzes variants of reward normalization and regularization.
result GRPO amplifies policy success, converging to a fixed point exceeding the reference.
Classifies soap film surfaces with vertical potentials.
problem Classifying soap film surfaces with vertical potentials.
method Variational characterization of n-elastic curves. result Obtains a full description of n-elastic curves. In [13], a new quasi-local energy is introduced for spacetimes with a non-zero cosmological constant. In this article, we study the small sphere limit of this newly defined quasi-local energy for spacetimes with a negative cosmological constant. For such spacetimes, the anti de-Sitter space is used as the reference for…
Two-sample tests improve on existing methods for microtubule data.
problem Testing differences between two groups of filament data.
method Optimal lifts and manifold stability theorem applied to microtubule data.
result New tests outperform existing methods on simulated and real data.
Study asset pricing with reference-dependent preferences, finding matching equity premia.
problem Understanding asset pricing under reference-dependent preferences.
method Discrete-time consumption-based capital asset pricing model with reference-dependent preferences.
result Models can generate equity premia matching empirical estimates, showing procyclical price-dividend ratio and countercyclical equity premium.
New KL-divergence for Gaussian distributions based on Wasserstein geometry.
problem Computing KL-divergence for Gaussian distributions efficiently.
method Introducing WKL-divergence based on Wasserstein geometry.
result WKL-divergence evaluates to squared distance between points for Dirac measures.
New MGCPP model for order flow in financial markets.
problem Modeling order flow dynamics in financial markets.
method Developed MGCPP, proved LLN and FCLTs, applied to real data.
result Validated MGCPP model with real trading data.
The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies, gauge group extensions, and 3-cocycles. The unifying concept is the classical o…
This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fi…
Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow…
Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven geometry compression method for static point clouds based on learned convolutional tra…
Provides an overview of Bartnik's quasi-local mass.
problem Understanding Bartnik's quasi-local mass.
method Surveys results on Bartnik's quasi-local mass.
result Serves as an entry point and quick reference.
The paper studies critical points of horizontal energy functional in Riemannian foliations.
problem Analyzing critical points of horizontal energy functional in Riemannian foliations.
method Utilizing stress-energy tensor, establishing monotonicity formulas, and Jin-type theorems.
result Established monotonicity formulas for horizontally harmonic maps and transversally harmonic maps.
pyLOT library simplifies machine learning on 3D point clouds via linearized optimal transport.
problem Performing machine learning tasks on 3D point clouds.
method Linearized optimal transport (LOT) to embed distributions into Hilbert space, enabling linear machine learning.
result Downstream tasks on embedded representations are simplified to linear operations.
New method for pricing SOFR futures options, solving both American and Asian exercise styles.
problem Lack of pricing models for SOFR futures options post-LIBOR transition.
method Developed a new version of the GIT method to solve semi-analytically.
result Obtained option prices, exercise boundaries, and Greeks for American and Asian options.
Rectifies flat singular points of area-minimizing currents with singularity degree > 1.
problem Rectifying flat singular points of area-minimizing currents with singularity degree > 1.
method Subdividing singular points based on singularity degree and proving rectifiability of points with singularity degree > 1.
result The set of points with singularity degree > 1 is (m-2)-rectifiable.
We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for o…
Active learning aims to train a classifier as fast as possible with as few labels as possible. The core element in virtually any active learning strategy is the criterion that measures the usefulness of the unlabeled data based on which new points to be labeled are picked. We propose a novel approach which we refer to …