arXiv research

Proposes SCR-Apriori for efficient mining of SCR-patterns.

In this article, we focus on distributed Apriori-based frequent itemsets mining. We present a new distributed approach which takes into account inherent characteristics of this algorithm. We study the distribution aspect of this algorithm and give a comparison of the proposed approach with a classical Apriori-like dist…

In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential. We also discuss some local versions of these estimates which can be of independent interest.

New geometric approach gives apriori estimate for optimal transport maps.

This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.

It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In addition, we obtain an apriori bound on the curvature of stationary vacuum soluti…

Methodology for learning sparse models using all multiplicative interactions efficiently.

The aim of this paper is to give a proof the Frankel conjecture by using the Kahler Ricci flow alone without assuming apriori the existence of Kahler Einstein metrics. However, there is an essential difference between the real case and the Kahler case. I didn't realize this difference in the calculation of the previous…

We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary to curves without boundary. Our method is new and geometric and…

Subspace clustering, the task of clustering high dimensional data when the data points come from a union of subspaces is one of the fundamental tasks in unsupervised machine learning. Most of the existing algorithms for this task require prior knowledge of the number of clusters along with few additional parameters whi…

We consider the mean curvature flow of a closed hypersurface in the complex or quaternionic projective space. Under a suitable pinching assumption on the initial data, we prove apriori estimates on the principal curvatures which imply that the asymptotic profile near a singularity is either strictly convex or cylindric…

Paper refines Chen-Cheng's estimates for Kähler metrics.

The purpose of this paper is to exhibit a quantitative stability result for the class of Möbius transformations of $\mathbb{S}^{n-1}$ when $n\geq 3$. The main estimate is of local nature and asserts that for a Lipschitz map that is apriori close to a Möbius transformation, an average conformal-isoperimetric type of def…

This paper connects graph curvature to community structure.

We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact $n$-dimensional manifold which has nonnegative Ricci curvature and strictly convex boundary. When $n=3$, this implies apriori area and curvature estimates for these minimal surfaces in terms of the …

Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper, we propose an approach based on semi-definite relaxations, which does not require…

It has been shown in \cite{DPSU} that, under some additional assumptions, two simple domains with the same scattering data are equivalent. We show that the simplicity of a region can be read from the metric in the boundary and the scattering data. This lets us extend the results in \cite{DPSU} to regions with the same …

In this paper, we generalize our apriori estimates on cscK(constant scalar curvature Kähler) metric equation to more general scalar curvature type equations (e.g., twisted cscK metric equation). As applications, under the assumption that the automorphism group is discrete, we prove the celebrated Donaldson's conjecture…

Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.

We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, fo…

Temporal Pattern Mining (TPM) is the problem of mining predictive complex temporal patterns from multivariate time series in a supervised setting. We develop a new method called the Fast Temporal Pattern Mining with Extended Vertical Lists. This method utilizes an extension of the Apriori property which requires a more…

Safe screening rules reduce computation time in logistic regression with $\ell_0-\ell_2$ regularization.

A new method for faster optimization of noisy functions.

Safe screening rules reduce $\ell_0$-regression computation by fixing 76% of variables.

Algorithm identifies nearest mode in noisy data.

Recursive prediction of graph signals with new nodes added.

Biological research often involves testing a growing number of null hypotheses as new data is accumulated over time. We study the problem of online control of the familywise error rate (FWER), that is testing an apriori unbounded sequence of hypotheses (p-values) one by one over time without knowing the future, such th…

The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective objective functions (ignoring the uncertainty in the model space), require the apriori…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only continuous and can vary; the curves are only assumed to have fixed ``topological type'', …

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 $e^Φ = \det D^2 Φ$ on proper convex cones. We…

Human explanations of high-level decisions are often expressed in terms of key concepts the decisions are based on. In this paper, we study such concept-based explainability for Deep Neural Networks (DNNs). First, we define the notion of completeness, which quantifies how sufficient a particular set of concepts is in e…

Quantifying the value of data is a fundamental problem in machine learning. Data valuation has multiple important use cases: (1) building insights about the learning task, (2) domain adaptation, (3) corrupted sample discovery, and (4) robust learning. To adaptively learn data values jointly with the target task predict…

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space $H_1$. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Mar…

To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…

New algorithm finds k-centers from noisy distance estimates.

Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.

Deep learning models are known to be overconfident in their predictions on out of distribution inputs. There have been several pieces of work to address this issue, including a number of approaches for building Bayesian neural networks, as well as closely related work on detection of out of distribution samples. Recent…

Strong worst-case performance bounds for episodic reinforcement learning exist but fortunately in practice RL algorithms perform much better than such bounds would predict. Algorithms and theory that provide strong problem-dependent bounds could help illuminate the key features of what makes a RL problem hard and reduc…

Compactness theorem for Riemannian manifolds with volume and curvature bounds.

MAntRA combines machine learning and Bayesian methods for time-dependent reliability analysis of unknown systems.

We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication constrained channels. We propose the design of distributed quantization schemes sp…

Training classification models on imbalanced data tends to result in bias towards the majority class. In this paper, we demonstrate how variable discretization and cost-sensitive logistic regression help mitigate this bias on an imbalanced credit scoring dataset, and further show the application of the variable discret…

A new method balances model quality and Byzantine robustness in Federated Learning.

The paper introduces a method to learn models with built-in explanations.

Study stability of rigid motions and Möbius transformations on spheres, proving new rigidity estimates.

Paper proposes a model-free algorithm for CMDPs with long-term constraints, achieving optimal regret bounds.

New algorithm tackles constrained Markov decision processes with peak constraints.

It is crucial to provide compatible treatment schemes for a disease according to various symptoms at different stages. However, most classification methods might be ineffective in accurately classifying a disease that holds the characteristics of multiple treatment stages, various symptoms, and multi-pathogenesis. More…