In the paper, we prove that a Moran set is homeomorphic to the hyperbolic boundary of the representing symbolic space in the sense of Gromov, which generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009), 1777-1795]. Moreover, by making use of this, we establish the Lipschitz equivalence of a class…
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48 results for “Moran sets”
The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.
problem Extending the measure preserving property to Moran sets.
method Analyzing bi-Lipschitz maps between Moran sets.
result Bi-Lipschitz maps between Moran sets preserve measure locally.
Machine learning models perform better with location coordinates alone, not Moran Eigenvectors.
problem Improving machine learning models for spatial data.
method Examined Moran Eigenvectors as additional spatial features in machine learning models using synthetic datasets.
result Machine learning models using only location coordinates achieve better accuracies than eigenvector-based approaches.
Study expands multiclass classification models with new rates and partial concept classes.
problem Multiclass classification with a bounded number of labels under various conditions.
method Extends traditional PAC model to distribution-dependent and data-dependent learning rates, characterizes optimal rates for universal and partial concept classes.
result Characterizes three types of learning rates (exponential, linear, arbitrarily slow) for fixed distributions and complexity measures for partial concept classes.
New operations match Steenrod squares on Khovanov homology.
problem Matching Steenrod squares with operations on Khovanov homology.
method Applied cup-i products to Khovanov functor and proved agreement with Steenrod squares.
result Lipshitz-Sarkar's Sq^2 agrees with Morán's sq^2.
SXL embeds spatial autocorrelation into neural networks for better geographic data learning.
problem Difficulties in learning spatial effects for neural networks in geographic data.
method SXL uses auxiliary tasks and autoregressive embeddings to learn spatial autocorrelation.
result SXL improves neural network training in unsupervised and supervised learning tasks.
This work proves DP learnability implies online learnability for general classification tasks.
problem Link between differential privacy and online learning for general classification tasks.
method Establishes Ramsey-type theorems for trees to prove DP learnability implies online learnability.
result DP learnability implies online learnability for general classification tasks.
Study optimal rates for multiclass classification, resolving open questions.
problem Optimal rates for multiclass classification with any label space.
method Establishes optimal rates for all hypothesis classes, defining new tree structures.
result Optimal rates for multiclass classification with no infinite DSL trees.
Study online multiclass classification under bandit feedback, extending previous results.
problem Online multiclass classification with bandit feedback, focusing on label space unboundedness.
method Extend Daniely and Helbertal's results, show necessity and sufficiency of Bandit Littlestone dimension for learnability.
result Sequential uniform convergence is necessary but not sufficient for bandit online learnability.
Theory extends optimal learning rates without realizability assumption.
problem Agnostic binary classification without realizability assumption.
method Identifies tetrachotomy of optimal rates and combinatorial structures.
result Optimal universal rates for binary classification in agnostic setting.
SX-GeoTree improves spatially coherent explanations in geospatial regression trees.
problem Capturing spatial dependence and producing robust explanations in tabular prediction models.
method Integrates three objectives: impurity reduction, spatial residual control, and explanation robustness via modularity maximization on a consensus similarity network.
result Improves residual spatial evenness and doubles attribution consensus (modularity: Fujian 0.19 vs 0.09; Seattle 0.10 vs 0.05).
We give an algorithmically efficient version of the learner-to-compression scheme conversion in Moran and Yehudayoff (2016). In extending this technique to real-valued hypotheses, we also obtain an efficient regression-to-bounded sample compression converter. To our knowledge, this is the first general compressed regre…
Study improves resilience against adversarial clean-label attacks in real and noisy settings.
problem Ensuring accurate predictions in the presence of adversarial clean-label samples.
method Sequential learning from a stream of i.i.d. data, allowing abstention for uncertain predictions.
result Theoretical analysis and adaptations for the agnostic setting with a clean-label adversary and noise.
We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if and are groups with asymptotic property C, then both and have asymptotic property C. We also prove that a group~ has asymptotic property C i…
Improved mistake bounds for transductive online learning.
problem Quantifying the power of unlabeled data in online learning.
method Proving lower and upper bounds on transductive mistake bounds.
result Exponential improvement in mistake bounds for transductive learning.
This work proves lower bounds on a greedy teaching set construction algorithm.
problem Characterize the best-case teaching dimension of a concept class.
method A greedy algorithm that iteratively adds points to the teaching set to restrict the concept class the most.
result Lower bounds on the performance of the greedy approach for small k, extending up to k ≤ c*d for small constant c.
We obtain the first positive results for bounded sample compression in the agnostic regression setting with the loss, where . We construct a generic approximate sample compression scheme for real-valued function classes exhibiting exponential size in the fat-shattering dimension but independen…
New findings show limitations in converting private learning to online learning efficiently.
problem Limitations in converting private learning to online learning efficiently.
method Assuming one-way functions, we show an efficient conversion from pure-private learners to online learners is impossible.
result Efficient conversion from pure-private learners to online learners is impossible under certain assumptions.
This study analyses, through cross-section estimation methods, the influence of spatial effects in the conditional product convergence in the parishes' economies of mainland Portugal between 1991 and 2001 (the last year with data available for this spatial disaggregation level). To analyse the data, Moran's I statistic…
New algorithm learns halfspaces almost optimally with fewer queries.
problem Learning halfspaces with minimal queries.
method Randomized linear decision tree of depth O(d log |X|).
result First nearly optimal solution for active learning of halfspaces.
Counterexamples show Salter's question on Burau image is negative for n=4.
problem Conditions for a matrix to be in the Burau image of .
method Analyzing the central quotient and using counterexamples.
result The central quotient of the Burau image group does not coincide with the central quotient of a specific subgroup of the unitary group for .
The consideration of spatial effects at a regional level is becoming increasingly frequent and the work of Anselin (1988), among others, has contributed to this. This study analyses, through cross-section estimation methods, the influence of spatial effects in productivity (product per worker) in the NUTs III economic …
This study analyses, through cross-section estimation methods, the influence of spatial effects in productivity (product per worker), at economic sectors level of the NUTs III of mainland Portugal, from 1995 to 1999 and from 2000 to 2005 (taking in count the data availability and the Portuguese and European context), c…
This study analyses, through cross-section estimation methods, the influence of spatial effects and human capital in the conditional productivity convergence (product per worker) in the economic sectors of NUTs III of mainland Portugal between 1995 and 2002. To analyse the data, Moran's I statistics is considered, and …
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
New study on replicability and stability in machine learning algorithms.
problem Ensuring consistent results in machine learning models without fixing randomness.
method Introduced global stability and list replicability concepts, proving their equivalence and boosting list replicability.
result Global stability can only be achieved weakly, while list replicability can be boosted to achieve high probability of consistent results.
New combinatorial dimension VCL refines learning curve theory.
problem Explaining the behavior of learning curves for specific distributions.
method Introducing combinatorial dimension VCL to characterize strong minimax lower bounds.
result Learning rate can be decomposed into linear and exponential components.
Study shows Julia sets and gasket limit sets are quasiconformally different.
problem Quasiconformal non-equivalence of Julia sets and gasket limit sets.
method Proved quasiconformal non-equivalence of Julia sets and gasket limit sets.
result Julia sets and gasket limit sets are quasiconformally different.
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
The paper analyzes set-to-set matching with neural networks, focusing on theoretical generalization.
problem Theoretical analysis of set-to-set matching with neural networks.
method Generalization error analysis of set-to-set matching with neural networks.
result Theoretical insights into the behavior of set-to-set matching models.
Generative model learns to autoencode and generate sets of images.
problem Learning to represent and generate sets of images with unknown number of sets.
method Set Distribution Networks (SDNs) learn set encoder, discriminator, generator, and prior.
result SDNs can reconstruct and generate sets of images with preserved attributes.
Study on cold and freezing sets in digital images.
problem Properties of cold sets in digital images.
method Analysis of properties and relationships between cold and freezing sets.
result Examined relationships between cold and freezing sets.
Paper solves whether zero sets are mapping degree sets.
problem Whether finite sets containing zero are mapping degree sets.
method Examined oriented closed connected manifolds of the same dimension.
result Affirmative answer given for both integer and rational settings.
Matching two different sets of items, called heterogeneous set-to-set matching problem, has recently received attention as a promising problem. The difficulties are to extract features to match a correct pair of different sets and also preserve two types of exchangeability required for set-to-set matching: the pair of …
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give an exa…
Study dynamics and topology of flows near non-saddle sets or W-sets.
problem Understanding the dynamics and topology of flows near specific invariant sets.
method Cohomological relations and global properties analysis.
result Dynamical classification of surfaces and robustness of non-saddle-sets.
The study explores mapping degree sets and their properties for manifolds.
problem Understanding the structure and properties of mapping degree sets for manifolds.
method Analyzes the properties of mapping degree sets and their relationships with self-mapping degree sets.
result Not every multiplicative set containing 0,1 is a self-mapping degree set.
Current approaches for predicting sets from feature vectors ignore the unordered nature of sets and suffer from discontinuity issues as a result. We propose a general model for predicting sets that properly respects the structure of sets and avoids this problem. With a single feature vector as input, we show that our m…
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the o…
Deep Sets approximates functions on sets with high-dimensional latent space.
problem Modeling functions of sets (permutation-invariant functions).
method Deep Sets, a method known to be a universal approximator for continuous set functions.
result Deep Sets' universal approximation property is only guaranteed with a sufficiently high-dimensional latent space.
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
A stability-based method selects the most desirable conformal prediction set.
problem Selecting the most desirable conformal prediction set from multiple valid sets invalidates coverage guarantees.
method A stability-based approach that ensures coverage for the selected prediction set.
result The stability-based approach maintains coverage guarantees for the selected prediction set.
The paper links set cuspidality to function regularity and flatness.
problem Linking set cuspidality to function regularity and flatness.
method Analyzes arc-smooth functions and their properties on various sets.
result Establishes a precise link between set cuspidality and function regularity.
This work establishes properties on diffeological structures for set-valued maps and measures.
problem Establish rigorous properties on diffeological structures for set-valued maps and measures.
method Using diffeologies, the authors link various structures including set-valued maps, relations, gradients, measures, and shape analysis.
result Established rigorous properties on sample diffeologies.
Causal Set Theory's Hauptvermutung is resolved in two ways, one of which is true.
problem Formulating and resolving the Hauptvermutung in Causal Set Theory.
method Two mathematically well-defined formulations of the Hauptvermutung, one of which is true.
result The Hauptvermutung is true when finite sets are replaced by countable sets.
This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding interpolations of probability distributions. We also demonstrate a preliminary so…