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.
Bayesian evidence computation revisited for model selection with improper priors.
Proposes a new SPVM model for RVM with more flexible priors.
The paper discusses the impact of prior densities on Bayesian model selection.
New GP kernels avoid mean reversion without losing smoothness.
The study classifies singularities in discrete improper affine spheres.
In this paper we consider convex improper affine maps of the 3-dimensional affine space and classify their singularities. The main tool developed is a generating family with properties that closely resembles the area function for non-convex improper affine maps.
Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the…
The paper generalizes offset Rademacher complexities to convex and non-convex problems.
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross caps never appear as the singularities on indefinite improper affine spheres and so…
Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefini…
The study classifies certain types of incomplete surfaces with low curvature.
We give a conformal representation for indefinite improper affine spheres which solve the Cauchy problem for their Hessian equation. As consequences, we can characterize their geodesics and obtain a generalized symmetry principle. Then, we classify the helicoidal indefinite improper affine spheres and find a new family…
There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dime…
Framework evaluates the impact of prior knowledge in deep learning models.
New DEC variant improves sample complexity bounds in decision making.
We give the best possible upper bound for the number of exceptional values of the Lagrangian Gauss map of complete improper affine fronts in the affine three-space. We also obtain the sharp estimate for weakly complete case. As an application of this result, we provide a new and simple proof of the parametric affine Be…
We study the Automatic Relevance Determination procedure applied to deep neural networks. We show that ARD applied to Bayesian DNNs with Gaussian approximate posterior distributions leads to a variational bound similar to that of variational dropout, and in the case of a fixed dropout rate, objectives are exactly the s…
In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and improper noninformative priors to be objective in the elicitation of parameter prior…
Improper affine spheres have played an important role in the development of geometric methods for the study of the Hessian one equation. Here, we review most of the advances we have made in this direction during the last twenty years.
New algorithm reduces online logistic regression regret without exponential constant.
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an …
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in operations, where…
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in netw…
We study the question of learning an adversarially robust predictor. We show that any hypothesis class with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes with finite VC…
Study shows improper learning can outperform proper learning in misspecified models.
New active learning framework for multiclass classification beyond realizability assumption.
We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvatureand for developable s…
Given a Lagrangian submanifold of the affine symplectic -space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension , both of whose sets of singularities contain . Although these improper affine spheres (IAS) always present other singularities away fro…
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and require only poly-logarithmically many calls to the approximation oracle per it…
Extended Ville's inequality for nonintegrable supermartingales.
Semi-supervised learning is a model training method that uses both labeled and unlabeled data. This paper proposes a fully Bayes semi-supervised learning algorithm that can be applied to any multi-category classification problem. We assume the labels are missing at random when using unlabeled data in a semi-supervised …
Two machine learning models detect anomalies in ER claims, saving up to 40% in improper payments.
Bornological metrics on groups are studied, showing equivalence classes and constructing non-equivalent improper metrics.
Study shows memory needs grow with task sequence length in continual learning.
Study shows inefficiency of sparse linear regression learning with fewer than Ω(k^2) samples.
Learning linear predictors with the logistic loss---both in stochastic and online settings---is a fundamental task in machine learning and statistics, with direct connections to classification and boosting. Existing "fast rates" for this setting exhibit exponential dependence on the predictor norm, and Hazan et al. (20…
Efficiently learns complex Boolean functions under Gaussian distributions.
New insights into learning from only positive examples.
New bounds for non-convex estimators without Bernstein condition.
Author presents the second variational formula for statistical biharmonic maps.
Paper explores rate-preserving reductions between Blackwell approachability and no-regret learning.
The paper studies a new class of affine maximal surfaces with singularities.
The nonzero level sets in -dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian determinant of the function is equal to a nonzero constant multiple of the th power of the function. The exponentials of the characteristic polynomials of certa…
We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missi…
Non-proper surface group action on product of trees found.
Overparameterized MLR fits hyper-curves, improving model robustness.
We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups associated with discrete indefinite affine spheres. In particular we show that a discrete indefinite improper affine sphere can be constructed …
One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods…