Paper recovers lattice signal partitions efficiently.
problem Estimating lattice partition from noisy data.
method Uses dyadic CART for computationally-efficient partition recovery.
result Consistently estimates partition with optimal error rate.
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48 results for “dyadic partition”
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
problem Capturing super-dyadic interactions in k-uniform hypergraphs.
method Tensor-based representation and tensor eigenvalue decomposition for capturing interactions.
result Improved min-cut solution on 2-uniform hypergraphs (graphs) compared to standard spectral partitioning.
Deep Nonparametric Estimation of Discrete Conditional Distributions via Smoothed Dyadic Partitioningstat.ML
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques: dyadic partitioning and graph-based smoothing of the discrete space. By recursivel…
Proposed by Donoho (1997), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article we define and study Dyadic CART and a closely related estimator, namely Optimal Regression Tree (ORT), in the contex…
Study predicts internet-based treatment effects for GPPPD based on dyadic coping.
problem Identifying which patients will benefit most from internet-based GPPPD treatment.
method Developed a multivariable decision tree model using recursive partitioning.
result Predicts large effects for high dyadic coping patients, small effects for low dyadic coping patients.
Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees…
Global subelliptic estimates for geometric Kramers-Fokker-Planck operators on closed manifoldsmath.AP
Proves subelliptic estimates for geometric Kramers-Fokker-Planck operators on closed manifolds.
problem Proving subelliptic estimates for a specific class of operators on closed manifolds.
method Significantly different method from previous works, using dyadic partition and local analysis in position variable.
result Maximal subelliptic estimates with control of constants in high and low friction regimes.
Develops a personalized reinforcement learning algorithm for dyadic health interventions.
problem Personalizing health interventions for dyadic relationships in mobile health.
method Dyadic Reinforcement Learning (dyadic RL), a Bayesian and hierarchical online algorithm.
result Established a regret bound and demonstrated empirical performance through simulations and real data.
Graph-Valued Regressionstat.ML
Undirected graphical models encode in a graph the dependency structure of a random vector . In many applications, it is of interest to model given another random vector as input. We refer to the problem of estimating the graph of conditioned on as ``graph-valued regression.'' In this pap…
Method estimates treatment effects in dyadic data with unknown confounders.
problem Estimating treatment effects in dyadic data with unobserved confounders.
method Neighborhood kernel smoothing method for graphon estimation.
result Derives rate of convergence for estimator and demonstrates test size control.
The paper develops a cross-validation method for improving signal denoising techniques.
problem Improving signal denoising methods for nonparametric regression.
method Develops a general cross-validation framework for signal denoising and applies it to Trend Filtering and Dyadic CART.
result Cross validated versions of Trend Filtering and Dyadic CART achieve nearly optimal convergence rates.
Develop conformal prediction for dyadic regression under complex missingness.
problem Conformal prediction for dyadic regression under complex missingness mechanisms.
method Developing general technical tools and conformal prediction procedures for dyadic regression under complex missingness.
result Establishing asymptotic validity of weighted conformal prediction under a nonparametric graphon model for missingness mechanism.
Variational autoencoder is a powerful deep generative model with variational inference. The practice of modeling latent variables in the VAE's original formulation as normal distributions with a diagonal covariance matrix limits the flexibility to match the true posterior distribution. We propose a new transformation, …
New framework tackles fairness in link prediction beyond demographic parity.
problem Systemic biases in link prediction can exacerbate societal inequalities.
method Formalizes limitations of existing fairness evaluations and proposes a new framework.
result Proposes a lightweight post-processing method combined with decoupled link predictors.
Dyadic Data Prediction (DDP) is an important problem in many research areas. This paper develops a novel fully Bayesian nonparametric framework which integrates two popular and complementary approaches, discrete mixed membership modeling and continuous latent factor modeling into a unified Heterogeneous Matrix Factoriz…
Paper introduces a method for generating interlocutor-aware facial gestures in dyadic settings.
problem Generating appropriate non-verbal behavior for conversational agents in dyadic settings.
method Probabilistic method using multi-modal cues from the interlocutor to synthesize facial gestures.
result The model successfully leverages multi-modal input from the interlocutor to generate more appropriate behavior.
Efficient algorithm computes knot invariants quickly.
problem Computing finite type invariants efficiently for knots.
method Create look-up tables for subdiagrams indexed by dyadic intervals, then compute invariants in time.
result Finite type invariants can be computed on an -crossing knot in time, significantly faster than previous methods.
The paper examines logistic regression in sparse network settings, improving inference under varying degrees of dyadic dependence.
problem Improving inference in logistic regression with sparse network data.
method Sparse network asymptotics, martingale central limit theorem, variance decomposition.
result Sparse network asymptotics lead to better variance estimators for logistic regression.
In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to com…
Revisiting Matrix Sketching in Linear Bandits: Achieving Sublinear Regret via Dyadic Block Sketchingcs.LG
New method reduces linear regret in high-dimensional bandit problems.
problem Heavy spectral tails in streaming matrices lead to linear regret in sketch-based linear bandits.
method Dyadic Block Sketching, a multi-scale matrix sketching approach.
result Achieves sublinear regret bounds without prior knowledge of streaming matrix properties.
Algorithm selection (AS) deals with selecting an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem, e.g., choosing solvers for SAT problems. Benchmark suites for AS usually comprise candidate sets consisting of at most tens of algorithms, whereas in combi…
New method distinguishes predictive distribution estimators in high-dimensional inputs.
problem Difficulty in evaluating predictive distributions for high-dimensional inputs.
method Introduces dyadic sampling to focus on predictive distributions associated with pairs of inputs.
result Demonstrates efficient distinction of predictive distribution estimators in high-dimensional examples.
We build polyhedral complexes in Rn that coincide with dyadic grids with different orientations, while keeping uniform lower bounds (depending only on n) on the flatness of the added polyhedrons including their subfaces in all dimensions. After the definitions and first properties of compact Euclidean polyhedrons and c…
While a user's preference is directly reflected in the interactive choice process between her and the recommender, this wealth of information was not fully exploited for learning recommender models. In particular, existing collaborative filtering (CF) approaches take into account only the binary events of user actions …
In self-organizing networks, topology and dynamics coevolve in a continuous feedback, without exogenous driving. The World Trade Network (WTN) is one of the few empirically well documented examples of self-organizing networks: its topology strongly depends on the GDP of world countries, which in turn depends on the str…
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country took action toward country at time "---known as dyadic events---in order to form an…
New method for efficient ERG fitting on large graphs.
problem Fitting non-trivial ERGs on large graphs.
method Fast matrix block-approximation techniques for dyadic independence.
result Models can generate networks with similar properties to observed networks.
Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holesgr-qc
Global existence and decay for quasilinear wave equations on various spacetimes, including Kerr black holes.
problem Global existence and decay for quasilinear wave equations on asymptotically flat spacetimes.
method Dyadically localised nature and direct use of a blackbox linear inhomogeneous energy estimate on exactly stationary metrics.
result Global existence and decay for small-data solutions to quasilinear wave equations on a wide variety of spacetime backgrounds, including Kerr black holes.
We consider the problem of group testing with sum observations and noiseless answers, in which we aim to locate multiple objects by querying the number of objects in each of a sequence of chosen sets. We study a probabilistic setting with entropy loss, in which we assume a joint Bayesian prior density on the locations …
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of …
The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform …
New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
The study limits how many parts regular simplicial partitions can overlap.
problem Bounding the intersection number of regular simplicial partitions.
method Analyzing the properties of regular simplicial partitions.
result Established a maximum limit for the intersection number.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …
In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the und…
In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…
The study examines the balancedness of random partition models and finds the rich-get-richer characteristic is a result of model assumptions.
problem The balancedness of random partition models is largely neglected in the literature.
method Formulated a framework to define and study the balancedness of exchangeable random partition models, analyzed using product-form exchangeability and projectivity assumptions.
result The 'rich-get-richer' characteristic is an inevitable consequence of the model assumptions.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvaturemath.DG
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
problem Understanding Markov partitions for general hyperbolic flows.
method Rigorous construction of Markov partitions for geodesic flow on Riemann surfaces of constant negative curvature.
result Explicit forms of rectangles and local cross sections provided for the geodesic flow.
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including variants of multi-level methods and spectral clustering. We propose GAP, a Generaliz…
A survey of mass partitionsmath.CO
Survey of mass partition problems in geometry and topology.
problem Inducing partitions on measures or sets by dividing space.
method Recent progress in topology, discrete geometry, and computer science.
result Connections between different fields.
Rank-one partitioning: formalization, illustrative examples, and a new cluster enhancing strategycs.LG
New method unifies and formalizes data partitioning using a single vector.
problem Data partitioning and clustering methods.
method Rank-one matrix factorization and denoising of piecewise constant signals.
result Demonstrates robustness of denoising step in partitioning.
Locally isoperimetric partitions minimize perimeter in space.
problem Finding minimal perimeter partitions in space.
method Proving closure theorem to limit sequences of isoperimetric clusters.
result Examples of isoperimetric partitions in various dimensions.
Online BSP-Forest improves space partitioning for large-scale classification and regression.
problem Efficient space partitioning for large-scale classification and regression problems.
method Developed an online BSP-Forest framework that expands space coverage and refines partition structure in real-time.
result Guaranteed universal consistency for both classification and regression problems.
Space partitions of underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions re…
Study of Torelli groups of partitioned surfaces with bounds and asymptotic lengths.
problem Understanding Torelli groups of partitioned surfaces.
method Topological and dynamical analysis of Torelli groups of partitioned surfaces.
result Asymptotic translation lengths of Torelli groups of partitioned surfaces behave almost like the reciprocal of the Euler characteristic of the surface.
Interpersonal relations are fickle, with close friendships often dissolving into enmity. In this work, we explore linguistic cues that presage such transitions by studying dyadic interactions in an online strategy game where players form alliances and break those alliances through betrayal. We characterize friendships …