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.
MPT improves CNN and energy-based models' OOD detection and generalization.
We present a theoretical framework of probabilistic learning derived by Maximum Probability (MP) Theorem shown in the current paper. In this probabilistic framework, a model is defined as an event in the probability space, and a model or the associated event -- either the true underlying model or the parameterized mode…
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double sided HMM. This makes it possible to use ergodic theorems. As an applicatio…
Improves A/B testing by detecting minor treatment effects.
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We …
Quantum ML predicts data with improved speed and accuracy.
Novel proof shows continuity of optimal transport feasible set mapping.
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…
Deep neural networks can approximate any target probability distribution given certain conditions.
Proves a theorem in sub-Riemannian geometry using Carnot groups.
General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will p…
Quantum method generates unbiased samples from discrete graphical models.
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probabi…
Extends three circle theorem to almost Hermitian manifolds.
A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. By the third kind of Bayes' theorem, we can directly convert a Shannon's channel into an optimized semantic channel. When a sample is not big enough, we can use a truth function with paramete…
Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.
Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein …
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems transforms the search for a probability density into the solution of a differential…
MAXENT method outperforms ML in sparse data with specific prior correlations.
MEP-Net uses MEP to generate solutions from limited data.
According to a classical result of E.~Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the "hyperbolic" toric Kähler-Einstein equation on proper convex cones. We…
New algorithms minimize MMD to approximate probability measures efficiently.
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
New method calibrates reference distributions for bounded support.
We prove a Lorentzian splitting theorem with weakened curvature conditions.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
Modified lognormal distribution with flexible tails for skewed data.
New non-existence results for harmonic maps into perturbed cones.
The paper classifies translation surfaces in a specific hyperelliptic component and finds the maximum number of disjoint geodesics.
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived i…
The paper shows how MMD metrizes weak convergence for certain kernels.
Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to sc…
Maximizing withdrawal success in a pooled annuity fund with multiple annuitants.
New bounds for optimal transport using Gaussian processes and rate-distortion functions.
Anisotropic minimal graphs over half-spaces are flat.
New method estimates Schrödinger bridges using ML techniques.
The paper proposes a new probability distribution for rooted trees.
New causal versions of MaxEnt and PIR avoid paradoxical probability updates.
In this short note we extend Chow and Lu's advanced maximum principles for parabolic systems on closed manifolds to the case of compact manifolds with boundary, which also generalizes a Hopf type theorem of Pulemotov.
Paper introduces GSPMs for robust probability metrics.
The paper solves portfolio selection for complex preferences in continuous time.
Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…
Paper uses stats to predict treatment choice based on illness probability.
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way of coupling Brownian motions on two minimal surfaces. This coupling is then used …
Reduces quantifier variance with accuracy optimization of base classifier.