Develops methods to construct exchangeable sequences of random multisets.
problem Creating models for random multisets with unknown base measures.
method Uses exchangeable sequences of point processes and conditional-i.i.d. negative binomial processes.
result Provides constructions for negative binomial processes with random base measures.
The study describes a cell structure for multisets in a rectangle.
problem Understanding the space of multisets in a rectangle.
method Developed a piecewise Euclidean bi-simplicial cell structure.
result Connected to spaces of complex polynomials and permutahedra.
Improved set prediction model using multiset-equivariant operations and approximate implicit differentiation.
problem Existing set prediction models struggle with multisets and cannot represent certain functions.
method Introduced multiset-equivariance, improved DSPN with approximate implicit differentiation, and applied to CLEVR object property prediction.
result Significantly improved object property prediction on CLEVR dataset.
New model learns multisets to predict containment and sizes of differences.
problem Learning permutation invariant representations for flexible containment.
method Formalize multisets, propose training on predicting symmetric difference sizes.
result Model outperforms DeepSets on predicting containment and sizes of symmetric differences.
New invariants defined for framed knots and links.
problem Defining invariants for framed knots and links.
method Introducing birack brackets and categorifying their multiset.
result Quiver-valued invariant defined for framed knots and links.
Proposes a novel node embedding framework for graphs using Fisher Information.
problem Lack of theoretical understanding of attention-based GNNs.
method Uses hierarchical kernels and Fisher Information to learn node embeddings.
result Proposed method outperforms existing GNNs on node classification benchmarks.
Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.
problem Optimizing Nyström samples for kernel matrix approximation.
method Stochastic gradient descent applied to multisets of landmark points (Nyström samples) using a surrogate criterion (radial SKD).
result Local minimization of the radial SKD yields improved Nyström approximation accuracy.
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This …
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
New method achieves small-loss regret bounds in random-order model.
problem Online learning with adversarial loss functions in random order.
method Extending batch-to-online transformation, using average sensitivity and stability.
result Small-loss regret bounds of order ildeO(φ⋆(OPTT)). Optimizer memory affects learning rate sensitivity in shuffle order, impacting fine-tuning noise.
problem Optimizer memory affects the learning rate sensitivity in shuffle order, leading to fine-tuning noise.
method Isolated the mechanism of fixed-clock optimizer memory affecting the learning rate sensitivity in shuffle order, deriving a fit-free way to size the noise.
result Fixed-clock optimizers like AdamW produce a larger first-order noise channel compared to memoryless optimizers, affecting fine-tuning comparisons.
New methods estimate correspondence between point sets with outliers.
problem Estimating correspondence between two point sets with outliers.
method Random sample consensus algorithms for robust regression without correspondence.
result Theoretical guarantees verified in simulated data and demonstrated in a neuroscience application.
Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in…
New graph foundation models respect symmetries for broader applicability.
problem Tailored graph machine learning architectures limit broader applicability.
method Investigates symmetries for label and feature permutations, proving network universal approximator.
result Universal approximator on multisets respecting node and feature permutations.
Birack modules are modules over an algebra Z[X] associated to a finite birack X. In previous work, birack module structures on Z mod n were used to enhance the birack counting invariant. In this paper, we use birack modules over Laurent polynomial rings Z_n[q,1/q] to enhance the birack counting invariant, defining a cu…
Constructs non-isometric iso-length-spectral surfaces.
problem Creating non-isometric surfaces with identical geodesic lengths.
method Combining Sunada's construction with amalgams of hyperbolic surfaces.
result Found non-isometric surfaces with the same geodesic lengths.
Enhances knot invariants using bilinear forms on vector spaces.
problem Improving classical and virtual knot invariants.
method Uses bilinear forms on vector spaces indexed by pairs of elements of a finite quandle.
result New enhanced invariants of knots and links.
EP-GFlowNets parallelize GFlowNet training for large-scale Bayesian inference.
problem Prohibitive repeated evaluations of unnormalized distributions for large-scale posterior sampling.
method Divide-and-conquer approach with server learning from local models.
result EP-GFlowNets enable efficient parallel and federated Bayesian inference.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on the space of persistence diagrams generates relevant input features for a classifi…
We introduce an infinite family of quantum enhancements of the biquandle counting invariant we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle colored oriented knot and link diagrams with values in a commutative ring R using virtual crossings as smoothings, these invariants take the…
A new policy minimizes loss in high-volume, short-lived multi-armed bandit problems.
problem Minimizing loss in high-volume, short-lived multi-armed bandit problems.
method Proposed a Bayesian policy to minimize loss over a large class of prior distributions.
result Our policy outperforms existing methods by 4.32% in total duration and 7.48% in total number of click-throughs.
STAG injects noise into graph neural networks to improve performance.
problem Graph neural networks suffer from over-smoothing and limited discrimination.
method Introduces a stochastic aggregation framework (STAG) with adaptive noise injection.
result STAG models correct both over-smoothing and discrimination issues.
Profile entropy measures learnability and compressibility of discrete distributions.
problem Understanding the learnability and compressibility of discrete distributions.
method Investigates profile entropy, showing its role in estimation, inference, and compression.
result Profile entropy is a fundamental measure unifying estimation, inference, and compression.
First differentially private mechanism for anonymized histograms.
problem Protecting sensitive data in anonymized histograms.
method Proposes a differentially private mechanism for releasing anonymized histograms.
result Achieves near-optimal privacy utility trade-off in terms of number of items and privacy parameter.
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence c…
The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is a fundamental invariant of the topology of M via Mostow-Prasad Rigidity. Motivated by this, the second author and Reid defined a two-dimensional analogue of the geodesic length spectrum given by the multiset of isometry types of total…
Paper defines a new pseudometric for measuring consensus among subsets of relations.
problem Measuring consensus among subsets of relations.
method Introduces a new pseudometric and provides a concise restatement with a functor interpretation. Also, describes an algorithm to calculate the pseudometric bound efficiently.
result The pseudometric can be bounded without an expensive search of possible mappings, based solely on the dimensions of the relations.
Researchers describe a Ceresa class for tropical and topological curves, linking algebraic and cohomological perspectives.
problem Explicitly describe the Ceresa class for non-hyperelliptic curves.
method Combining algebraic, tropical, and topological perspectives, defining the Ceresa class for curves and surfaces.
result The Ceresa class is torsion in all settings: tropical curves, topological surfaces, and smooth algebraic curves over C((t)). Study circle actions on unitary manifolds with discrete fixed points.
problem Understanding circle actions on compact unitary manifolds with discrete fixed points.
method Prove relationships between weights at fixed points and derive results regarding the first equivariant Chern class and Hirzebruch χy-genus. result Derive a multigraph encoding fixed point data, leading to new insights into unitary S1-manifolds. New method for probabilistic modeling of integer submodular functions.
problem Lack of probabilistic modeling for integer submodular functions.
method Proposed Generalized Multilinear Extension and block-coordinate ascent algorithm.
result Demonstrated effectiveness and viability on real-world datasets.
Algorithm estimates covariance from noisy data efficiently.
problem Estimating covariance from a noisy set of points.
method Spectral techniques for list-decodable covariance estimation.
result Efficient algorithm with poly(1/α) sample and time complexity.
In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate hyperbolic polygons, i.e. relatively compact domains in the hyperbolic plane with…
Efficient algorithm for orthogonal canonical correlation analysis (OCCA).
problem Solving the OCCA problem with orthogonality constraints.
method Sub-maximization problem with self-consistent-field (SCF) iteration for trace-fractional structure and orthogonal linear projections.
result Proposed algorithm converges globally to a KKT point and is more efficient.
Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains are projected to a common space by linear transformations in order to search clos…
Sparse connectivity improves generalization in neural networks below the Edge of Stability.
problem Generalization guarantees for fully-connected networks fail at the Edge of Stability.
method Analyzed sparse connectivity's impact on generalization in two-layer ReLU networks.
result Sparse connectivity changes the effective constraint, leading to non-vacuous generalization bounds.
Paper improves likelihood estimation for discrete distributions.
problem Computing profile maximum likelihood for discrete distributions.
method New bounds on Bethe and Sinkhorn permanents for low rank matrices.
result Achieves an approximation factor of exp(-O(sqrt(n) log n)) in polynomial time.
The study examines property testing and estimation under non-identically distributed samples, finding necessary and sufficient sample complexities.
problem Property testing and estimation under non-identically distributed samples.
method Analysis of distributional property testing and estimation in settings with heterogeneous entities.
result Necessary and sufficient sample complexities for property testing and estimation under non-identically distributed samples.
This paper surveys various methods for dimensionality reduction and nearest neighbor search.
problem Efficiently reducing high-dimensional data to lower dimensions while preserving essential information.
method Linear and nonlinear random projections, including sparse random projections, random Fourier Features, and Random Kitchen Sinks.
result Various methods for dimensionality reduction and nearest neighbor search are explained and compared.
The paper studies how norms of random vectors are preserved by random projections.
problem Understanding how random matrix affects norms of random vectors.
method Proved the distribution of the norm of random vector is preserved by random projection.
result Random matrix preserves the distribution of the norm of random vectors with i.i.d. entries.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
problem Approximating Gaussian kernel efficiently for large datasets.
method Use of Haar orthogonal matrices to construct orthogonal random features and analyze their bias and variance.
result Orthogonal random features approximate a Bessel kernel, not the Gaussian kernel, with sharper bounds.
New methods improve prediction performance and reduce computation time in boosting and random forest models.
problem Improving prediction performance and reducing computation time in boosting and random forest models.
method Random tree depth injection approach for Boosting and Random Forests.
result The new methods can improve prediction performance and reduce computation time by up to 40%.
Proposes a method for modeling random objects in metric spaces using random effects.
problem Modeling random objects in non-Euclidean spaces with random effects.
method Nonlinear Fréchet-based algorithm for M-estimation.
result Consistent estimation of prediction target under random-effects formulation.
Enhances random forest performance with exogenous randomness.
problem Improving random forest performance through exogenous randomness.
method Developed non-asymptotic MSE expansions for individual trees and forests, identified two types of randomness, and conducted simulations.
result Exogenous randomness, particularly feature subsampling, reduces both bias and variance of random forests.
New random forest method provides optimal rates and confidence bands.
problem Improving random forest regression rates and constructing confidence bands.
method Proposed Ehrenfest centered purely random forests achieve optimal rates; used Gaussian approximation for supremum of empirical processes.
result Explicit asymptotic uniform confidence bands constructed for both random forest types.
Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös-Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about t…
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
Random subgroups of free groups are invariant only by inner automorphisms.
problem Understanding the structure of random subgroups in free groups.
method Analyzing splittings and automorphisms of random subgroups.
result Random subgroups of free groups are invariant only by inner automorphisms.