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.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
Paper certifies intersection of minimum-volume confidence sets for multinomial outcomes.
We develop an efficient algorithm to find confidence ellipsoids with volume guarantees in high dimensions.
Optimizes minimum-volume prediction sets for multivariate regression.
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
Paper compares two entropy concepts for finite presentation groups.
New method for NMF without tuning parameter.
We enumerate the small-volume manifolds that can be obtained by Dehn filling on Mom-2 and Mom-3 manifolds as defined by Gabai, Meyerhoff, and the author. In so doing we complete the proof that the Weeks manifold is the minimum-volume compact hyperbolic 3-manifold, as well as enumerating the 10 smallest one-cusped hyper…
Four hyperbolic 24-cell 4-manifolds with one cusp are identified.
Extends conformal prediction to contrastive learning for better coverage of positive samples.
We propose a non-parametric anomaly detection algorithm for high dimensional data. We first rank scores derived from nearest neighbor graphs on -point nominal training data. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as…
We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows topic modeling to be reformulated as finding the probability simplex that minimizes …
Paper proves min-vol NMF robust to noise under expanded condition.
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
A new method for SSMF improves upon existing algorithms.
This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of tail estimation techniques: univariate observations are viewed as all the more …
Study finds a minimum volume for vector fields on a punctured sphere.
Paper finds minimum volume for specific anti-de Sitter 3-manifolds.
We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a …
This is an expository paper on Mom-technology, describing the recent work of the authors in this area (found in arXiv:math/0606072, arXiv:0705.4325, and arXiv:0809.0346) concerning the use of Mom-technology to find the minimum-volume compact hyperbolic 3-manifold and the 10 smallest cusped hyperbolic 3-manifolds. In ad…
New method constructs confidence sets for GLMs via game theory.
New methods improve confidence set calibration in complex models.
Paper checks SSC for matrix factorizations using Gurobi.
We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to cons…
It was previously shown by the second author that every knot in is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot to be the minimum volume of any link in a natural class of alternating, hyperbolic links such tha…
ACORE improves hypothesis testing and confidence sets in likelihood-free inference.
New method optimizes offline linear bandits using different confidence sets.
Novel confidence sets improve linear bandit performance by adapting to unknown noise levels.
The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient a…
Improved regret bounds for logistic bandits via novel confidence set construction.
We shrink confidence sets for equivalent discrete distributions using permutation equivalence.
We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average -NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly…
Develops methods for valid and validated confidence sets in multiclass and multilabel prediction.
Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang…
Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition probabilities---which is usually constructed as a multi-dimensional confidence region. E…
Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discret…
Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift, the jump intensity and the …
Deep learning architectures have proved versatile in a number of drug discovery applications, including the modelling of in vitro compound activity. While controlling for prediction confidence is essential to increase the trust, interpretability and usefulness of virtual screening models in drug discovery, techniques t…
A universal framework for constructing confidence sets using sequential likelihood mixing.
Overlap between treatment groups is required for non-parametric estimation of causal effects. If a subgroup of subjects always receives the same intervention, we cannot estimate the effect of intervention changes on that subgroup without further assumptions. When overlap does not hold globally, characterizing local reg…
The paper finds a fundamental trade-off between confidence and efficiency in transductive conformal prediction.
Confidence-based deferral works well in many scenarios but fails in specific cases.
Study three types of uncertainty quantification for binary classification without distributional assumptions.
We classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces and they are all arithmetic, i.e., they are associated with quotients of the ball by an arithmetic lattice. Moreover, the asso…
This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3-manifolds. Using Mom technology, we prove that any one-cusped hyperbolic 3-manifold with volume <= 2.848 can be obtained by a Dehn filling on one of 21 cusped hyperbolic 3-manifolds. We also sho…
A general approach for anomaly detection or novelty detection consists in estimating high density regions or Minimum Volume (MV) sets. The One-Class Support Vector Machine (OCSVM) is a state-of-the-art algorithm for estimating such regions from high dimensional data. Yet it suffers from practical limitations. When appl…
Paper presents methods to create stock price confidence intervals using LSTM models.
The paper addresses the gap between theoretical and practical confidence set widths in universal inference.