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.
Paper introduces algorithms for explaining monotonic classifiers.
Study shows configuration spaces' homological dimension increases monotonically.
COMET learns monotonic neural networks by incorporating counterexamples.
Curve shortening flow increases annulus modulus.
GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.
Improves k-NN for monotonic data with robustness against noise.
The paper proves a transformation theorem under a monotone property of almost Euclidean factors of geodesic balls.
This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves which are simple or constant, and in which curves are pairwise disjoint. We show that, if the boundary of a Riemannian disc can be contracted th…
Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…
The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called loading monotonicity, is satisfied by premiums that appear in the literature. The inc…
Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty…
We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in . As an application, we derive a sharp geometric inequality for mean convex, star-shaped hypersurfaces which relates the volume enclosed by a hypersurface to a weighted total mean curvature of the hypers…
The paper extends the avoidance principle for mean curvature flows, proving new intersection dimension monotonicity results.
The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.
The paper proves the monotonicity of a modified Perelman's W-entropy for mean curvature flow.
This work is devoted to the study of parabolic frequency for solutions of the heat equation on Riemannian manifolds. We show that the parabolic frequency functional is almost increasing on compact manifolds with nonnegative sectional curvature, which generalizes a monotonicity result proved by C. Poon and by L. Ni. The…
New models ensure monotonicity in preference learning, improving accuracy especially with limited data.
New findings show privacy affects generalization error in a non-monotonic way.
Study de Rham homomorphism for Lipschitz cohomologies on metric simplicial complexes.
New quantity helps map homotopy classes in complex spaces.
The main purpose of this note is to construct two functionals of the positive solutions to the conjugate heat equation associated to the metrics evolving by the conformal Ricci flow on closed manifolds. We show that they are nondecreasing by calculating the explicit evolution formulas of these functionals. For the entr…
New algorithms avoid non-monotonic risk curves in statistical learning.
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. T…
Plotting a learner's average performance against the number of training samples results in a learning curve. Studying such curves on one or more data sets is a way to get to a better understanding of the generalization properties of this learner. The behavior of learning curves is, however, not very well understood and…
Monotonicity helps in safely optimizing unknown functions.
Adaptive learning rate improves FTRL's performance in online learning.
This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian…
A new learning rule consistently reduces error over data samples.
Investigates probability of error in structured thresholding bandit problems.
We propose some natural generalizations of Reidemeister moves that do not increase the number of crossings in the generated diagrams. Experimentations make us conjecture that this class of monotonic moves is complete for computing canonical forms and then deciding isotopy.
New method identifies causal order without sparsity assumptions.
ThiopheneIV is a new solver for implied volatility with proven monotonicity.
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimatio…
It is the aim of this article to determine curvature quantities of an arbitrary Riemannian monotone metric on the space of positive matrices resp. nonsingular density matrices. Special interest is focused on the scalar curvature due to its expected quantum statistical meaning. The scalar curvature is explained in more …
Proves existence and uniqueness of viscosity solutions to complex Hessian equations on compact Hermitian manifolds.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
A quaternionic contact (qc) heat equation and the corresponding qc energy functional are introduced. It is shown that the qc energy functional is monotone non-increasing along the qc heat equation on a compact qc manifold provided certain positivity conditions are satisfied.
In this paper, we mainly investigate continuity, monotonicity and differentiability for the first eigenvalue of the -Laplace operator along the Ricci flow on closed manifolds. We show that the first -eigenvalue is strictly increasing and differentiable almost everywhere along the Ricci flow under some curvature a…
The paper studies nodal sets of solutions to parabolic equations, proving finiteness and monotonicity properties.
This paper analyzes and improves monotonic accelerated algorithms like M-NAG and M-FISTA.
We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latter be…
The Cheeger constant increases under Ricci flow on spheres.
Two new methods improve monotonic constraint enforcement in regression and classification trees.
This paper introduces a novel approach for learning to rank (LETOR) based on the notion of monotone retargeting. It involves minimizing a divergence between all monotonic increasing transformations of the training scores and a parameterized prediction function. The minimization is both over the transformations as well …
In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property…
We analyze the sample complexity of the thresholding bandit problem, with and without the assumption that the mean values of the arms are increasing. In each case, we provide a lower bound valid for any risk and any -correct algorithm; in addition, we propose an algorithm whose sample complexity is of the same o…
The Softmax function on top of a final linear layer is the de facto method to output probability distributions in neural networks. In many applications such as language models or text generation, this model has to produce distributions over large output vocabularies. Recently, this has been shown to have limited repres…
We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also…