arXiv research

Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.

Develops monotone tree-based GAMI models using XGBoost.

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…

New method identifies causal order without sparsity assumptions.

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous…

The paper defines new geometric concepts on Riemannian manifolds and applies them to optimization problems.

Deep networks show less disorder and more monotonic behavior.

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. W…

Monotonic differentiable sorting networks improve upon previous methods.

In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in mach…

The paper studies Steklov eigenvalues in space forms and warped product manifolds, deriving bounds and monotonicity results.

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explici…

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

MCNet improves uncertainty calibration in online advertising by modeling complex relations and balancing performance.

Holonomy groups of metric connections converge in a monotonic way.

Monotonic policy improvement and off-policy learning are two main desirable properties for reinforcement learning algorithms. In this paper, by lower bounding the performance difference of two policies, we show that the monotonic policy improvement is guaranteed from on- and off-policy mixture samples. An optimization …

In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$, $p(x) \leq p(y)$. To understand the sample complexity of this problem, we intro…

Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that operate in non-monotonic orders; the model directly learns good orders, without any ad…

Stochastic control problems in finance often involve complex controls at discrete times. As a result numerically solving such problems, for example using methods based on partial differential or integro-differential equations, inevitably give rise to low order accuracy, usually at most second order. In many cases one c…

When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e…

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit …

We obtain an ordering of closed aspherical 4-manifolds that carry a non-hyperbolic Thurston geometry. As application, we derive that the Kodaira dimension of geometric 4-manifolds is monotone with respect to the existence of maps of non-zero degree.

We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where $p>1$ and $n\ge1$. We give a complete classification of stable and finite Morse index solutions (whether positive or sign changing), in the full exponent range. We also compute an…

Strong geodesic convex function and strong monotone vector field of order $m$ on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order $m$ for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…

The paper explores capital allocation using Euler formula with VaR and ES, revealing non-monotonicity and providing estimation methods.

Develops a first-order interior-point method for solving constrained variational inequalities.

Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.

New method calibrates neural network predictions for better reliability.

Zamolodchikov's c-theorem type argument (and also string theory effective action constructions) imply that the RG flow in 2d sigma model should be gradient one to all loop orders. However, the monotonicity of the flow of the target-space metric is not obvious since the metric on the space of metric-dilaton couplings is…

Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.

Study nondegenerate singularities in mean curvature flow.

New positive mass theorem for hyperbolic 3-manifolds using Green functions.

A new learning rule consistently reduces error over data samples.

Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do not rely on an underlying gradient estimate and are numerically stable. We analy…

The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.

New insights into variational inference using Monte Carlo estimates.

This paper shows how to learn variational inequalities fast with strong monotonicity.

Study on minimal surfaces with constraints on index and branching order.

The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.

Gradient descent dynamics in quadratic regression models are analyzed, revealing five phases: monotonic, catapult, periodic, chaotic, and divergent.

Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.

The paper addresses monotonicity in machine learning models for fairness and accountability.

Derives a new formula for optimal stopping problems with exploding derivatives.

We give a singular control approach to the problem of minimizing an energy functional for measures with given total mass on a compact real interval, when energy is defined in terms of a completely monotone kernel. This problem occurs both in potential theory and when looking for optimal financial order execution strate…

New tail dependence measures for stock indices.

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

The paper tackles non-monotonic learning performance and proposes algorithms to make models more monotone.