arXiv research

In-context learning solves PU classification without iterative optimization.

Improves PU learning for imbalanced data with practical AUL estimation and new training method.

We describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface $S$ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperpolic plane. We establish a bijection between …

New random forest algorithms for PU learning minimize risk directly.

The paper establishes risk bounds for PU learning with label noise.

New representations for surface groups in PU(2,1) are stable and larger than convex cocompact ones.

Self-PU combines self-training with PU learning for improved binary classification.

Study of Horn's problem in PU(n,1) for n≥1.

Smooth knots in complex hyperbolic plane limit sets to chains or R-circles.

A novel transfer learning framework combines multiple data sources for PU learning.

Meta-learning method improves PU classification performance.

We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1).

We present a novel approach to learn binary classifiers when only positive and unlabeled instances are available (PU learning). This problem is routinely cast as a supervised task with label noise in the negative set. We use an ensemble of SVM models trained on bootstrap resamples of the training data for increased rob…

Paper proposes a new loss function for PU learning without negative examples.

Study proposes a clustering and logistic regression algorithm for PU classification under Non-SCAR.

In binary classification, there are situations where negative (N) data are too diverse to be fully labeled and we often resort to positive-unlabeled (PU) learning in these scenarios. However, collecting a non-representative N set that contains only a small portion of all possible N data can often be much easier in prac…

A new method predicts true classes from positive and unlabeled data with additional labeled observations.

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…

Every element of PU(2,1) can be decomposed into at most 4 special elliptic isometries.

Discrete PU(1,1) representations of hyperelliptic groups are proven.

Recent advances in weakly supervised classification allow us to train a classifier only from positive and unlabeled (PU) data. However, existing PU classification methods typically require an accurate estimate of the class-prior probability, which is a critical bottleneck particularly for high-dimensional data. This pr…

The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles (revised version)" which gives simpler, clearer proofs of the transversality results,…

Paper proposes a method to compress deep learning models using PU setting and cloud data.

Proves $PU(n,1)$ is 1-taut, concluding studies of rank-one Lie groups.

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

Study on surface group representations in PU(2,1) leading to convex-cocompact examples.

Study character varieties for 3-punctured sphere group representations in PU(2,1).

Improved bounds on curve filling areas in Banach spaces, leading to rigidity of Pu's inequality.

We explore hybrid subgroups of certain non-arithmetic lattices in $\mathrm{PU}(2,1)$. We show that all of Mostow's lattices are virtually hybrids; moreover, we show that some of these non-arithmetic lattices are hybrids of two non-commensurable arithmetic lattices in $\mathrm{PU}(1,1)$.

We consider a certain hybridization construction which produces a subgroup of ${\rm PU}(n,1)$ from a pair of lattices in ${\rm PU}(n-1,1)$. Among the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$, we show that the hybrid of pairs of Fuchsian subgroups ${\rm PU}(1,1,\mathcal{O}_d)$ is a lattice when $d=1$ and $d=7…

This paper reviews PU learning evaluation methods and provides practical recommendations.

A new PU classifier PUAL tackles trifurcate data issues.

This research announcement gives a brief report of the main results in our paper "PU(2) monopoles, I: Regularity, Uhlenbeck compactness, and transversality" (Journal of Differential Geometry, to appear). We describe the existence of perturbations for the PU(2) monopole equations, yielding both useful transversality pro…

This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. The moduli space of solutions to t…

Positive--unlabeled (PU) learning considers two samples, a positive set P with observations from only one class and an unlabeled set U with observations from two classes. The goal is to classify observations in U. Class mixture proportion estimation (MPE) in U is a key step in PU learning. Blanchard et al. [2010] showe…

Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the program to prove this relation using a moduli space of PU(2) = SO(3) monopoles as a cobordism between the Donaldson moduli spac…

New model tackles PU data with better accuracy.

New method for PU learning with instance-dependent propensity scores.

We study representations of lattices of PU(m,1) into PU(n,1). We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex hyperbolic n-space. This allows us to give a differential geometric proof of rigidity …

The paper proposes methods to estimate positive examples and learn classifiers from mixed data.

Let $Γ$ be a non-uniform lattice in $PU(p,1)$ without torsion and with $p\geq2$. We introduce the notion of volume for a representation $ρ:Γ\rightarrow PU(m,1)$ where $m \geq p$. We use this notion to generalize the Mostow--Prasad rigidity theorem. More precisely, we show that given a sequence of representations $ρ_n:…

New PU ratio predicts long-term Bitcoin returns better than other methods.

Improved classifier for PU data using logistic regression.

Learning from positive and unlabeled data or PU learning is the setting where a learner only has access to positive examples and unlabeled data. The assumption is that the unlabeled data can contain both positive and negative examples. This setting has attracted increasing interest within the machine learning literatur…

We prove the existence of perturbations for the PU(2) monopole equations, yielding transversality on the complement of the anti-self-dual or reducible solutions, and the existence of an Uhlenbeck compactification for the moduli space of solutions to these perturbed PU(2) monopole equations. In December 1994, V. Pidstri…

A new systolic inequality with a remainder for the real projective plane.

Paper tackles leveraging unlabeled data for PU classification and robust generation.

New methods learn from PU data with non-representative positives.