A new model predicts dynamic O-D matrices using graph neural networks and Kalman filters.
problem Predicting dynamic O-D demand matrices from traffic flow data.
method Combines graph neural networks and Kalman filters to recognize spatial and temporal patterns.
result The proposed model outperforms other methods in various prediction scenarios.
New algorithms achieve stable and private predictions with reduced sample complexity.
problem Achieving stable and private predictions in binary classification.
method Developed new algorithms for stable and private prediction, reducing sample complexity.
result Achieved stable and private predictions with reduced sample complexity for VC dimension d d d . Proposes a new model to predict travel demand with zero-inflated and long-tail characteristics.
problem Sparse and long-tailed travel demand data with many zeros.
method Spatial-Temporal Tweedie Graph Neural Network (STTD) using Tweedie distribution.
result STTD provides accurate predictions and precise confidence intervals.
Improved SGD for non-strongly-convex regression with faster convergence.
problem Non-strongly-convex least squares regression problems.
method Modified accelerated gradient descent.
result Achieves optimal prediction error rates of O ( d / t ) O(d/t) O ( d / t ) and forgets initial conditions faster to O ( d / t 2 ) O(d/t^2) O ( d / t 2 ) . This paper proves IRM minimizes o.o.d. risk under certain conditions.
problem Deep networks can fail to generalize to new domains with different distributions.
method Proves IRM minimizes o.o.d. risk through a bi-level optimization problem.
result IRM minimizes o.o.d. risk under specific conditions.
New model predicts travel demand uncertainty with high accuracy.
problem Uncertainty and sparsity in sparse travel demand prediction.
method Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN).
result STZINB-GNN outperforms benchmarks in predicting travel demand uncertainty.
We consider a partial-feedback variant of the well-studied online PCA problem where a learner attempts to predict a sequence of d d d -dimensional vectors in terms of a quadratic loss, while only having limited feedback about the environment's choices. We focus on a natural notion of bandit feedback where the learner only…
RankSEG-RMA improves semantic segmentation efficiency and applicability.
problem Inconsistent or suboptimal semantic segmentation results due to argmax or thresholding.
method Developed RankSEG-RMA using reciprocal moment approximation to optimize Dice and IoU metrics.
result RankSEG-RMA reduces computational complexity to O(d) while maintaining comparable performance.
New algorithms adapt to both gradient norms and comparator norms in online learning.
problem Adapting to both gradient norms and comparator norms in online learning.
method Developed parameter-free and scale-free algorithms for unbounded online convex optimization.
result Improved regret bounds for scale-invariant online prediction with linear models.
StAD predicts divergence of diffusion and flow models without Jacobian computation.
problem Computing likelihood from diffusion and flow models is computationally expensive.
method Introduces StAD, a distillation method to predict divergence using Langevin-Stein operator.
result StAD predicts divergence with competitive variance and speed compared to existing methods.
LOO prediction method improves generalization guarantees for arbitrary datasets.
problem Understanding LOO error guarantees in fully transductive settings for arbitrary datasets.
method Median of Level-Set Aggregation (MLSA) for empirical-risk level sets.
result Multiplicative oracle inequality for LOO error with complexity scaling.
In this paper we study the topology of three different kinds of spaces associated to polynomial knots of degree at most d d d , for d ≥ 2 d\geq2 d ≥ 2 . We denote these spaces by O d \mathcal{O}_d O d , P d \mathcal{P}_d P d and Q d \mathcal{Q}_d Q d . For d ≥ 3 d\geq3 d ≥ 3 , we show that the spaces O d \mathcal{O}_d O d and P d \mathcal{P}_d P d are path connected and the …
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O ( d / n ) O(d/n) O ( d / n ) in bounded distributions. Combines fast evaluation with Bayes consistency in nearest neighbors.
problem Balancing fast evaluation time with Bayes consistency in nearest neighbors.
method Combines locality-sensitive hashing (LSH) with a missing-mass argument.
result Fast and Bayes-consistent classifier with comparable risk decay rates.
Let M n M^n M n be a complete noncompact K a ¨ \ddot{a} a ¨ hler manifold of complex dimension n n n with nonnegative holomorphic bisectional curvature. Denote by O \mathcal{O} O _d(M^n) t h e s p a c e o f h o l o m o r p h i c f u n c t i o n s o f p o l y n o m i a l g r o w t h o f d e g r e e a t m o s t the space of holomorphic functions of polynomial growth of degree at most t h es p a ceo f h o l o m or p hi c f u n c t i o n so f p o l y n o mia l g r o w t h o f d e g r ee a t m os t d o n on o n M^n . I n t h i s p a p e r w e p r o v e t h a t . In this paper we prove that . I n t hi s p a p er w e p r o v e t ha t dim_{\mathbb{C}}{\mathcal{O}}_d(…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates bina…
The standard actions of finite groups on spheres S^d are linear actions, i.e. by finite subgroups of the orthogonal group O(d+1). We prove that, in each dimension d>5, there is a finite group G which admits a faithful, topological action on a sphere S^d but is not isomorphic to a subgroup of O(d+1). The situation remai…
New algorithm speeds up HMC by generating a warm start in O(d^1/4) iterations.
problem Unclear how many iterations of HMC are needed for high-dimensional sampling.
method Developed a non-Metropolized HMC that generates a warm start in O(d^1/4) iterations, followed by Metropolized HMC.
result Final complexity of O(d^1/4) is the fastest algorithm for high-accuracy sampling under strong log-concavity assumptions.
Learning to approximate a separable function is hard, requiring many samples even with sparse networks.
problem Learning the separable function x ↦ ∑ i = 1 d x i 2 x \mapsto \sum_{i=1}^d x_i^2 x ↦ ∑ i = 1 d x i 2 with limited samples. method Sparse neural networks vs. dense neural networks, explicit regularization.
result The sample complexity for dense networks is O ( d 2.5 ) \mathcal{O}(d^{2.5}) O ( d 2.5 ) with explicit regularization, better than O ( d 4 ) \mathcal{O}(d^{4}) O ( d 4 ) . Improved log-concave sampling to O ( d 1 / 2 ) O(d^{1/2}) O ( d 1/2 ) with warm starts.
problem Sampling from strongly log-concave distributions efficiently.
method Warm starts and discretized underdamped Langevin diffusion.
result Achieved O ( d 1 / 2 ) O(d^{1/2}) O ( d 1/2 ) complexity for high-accuracy sampling. Active sampling algorithm for linear regression with various norms and improved query complexity.
problem Efficiently querying a few entries of a target vector for near optimal minimizers of linear regression.
method Lewis weight sampling and active sampling algorithms for different p p p norms. result Optimal query complexity for p ∈ ( 0 , 1 ) p \in (0,1) p ∈ ( 0 , 1 ) , 1 < p < 2 1<p<2 1 < p < 2 , and 2 < p < ∞ 2<p<\infty 2 < p < ∞ . Randomly chosen support makes sparse linear regression easy.
problem Sparse linear regression with random support.
method Random support selection for efficient prediction.
result Prediction error ε ε ε with N = e x t p o l y ( k , log d , 1 / ε ) N = ext{poly}(k, \log d, 1/ε) N = e x t p o l y ( k , log d , 1/ ε ) samples and e x t p o l y ( d , N ) ext{poly}(d,N) e x t p o l y ( d , N ) run-time. Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.
problem Learning Gaussian distributions while maintaining privacy.
method General framework for reducing DP estimation to non-private, polynomial-time algorithm for Gaussian learning.
result Matching sample complexity to information-theoretic upper bound for Gaussian learning.
Self-training improves weak classifiers in mixture models.
problem Improving weak classifiers in mixture models.
method Iterative self-training algorithm using pseudolabels and unlabeled data.
result Self-training converts weak learners to strong learners in mixture models.
GONs improve predictions of maximizers from noisy black-box functions.
problem Estimating maximizers of noisy black-box functions.
method Global Optimization Networks (GONs) composed of invertible and unimodal functions.
result GONs outperform convex fits, GPR, and DNNs in prediction accuracy.
Improved regret bound for adversarial bandit convex optimisation.
problem Minimizing regret in zeroth-order adversarial bandit convex optimisation.
method Identifying an improved exploratory distribution for convex functions.
result Proved minimax regret bound of O ( d 2.5 n log ( n ) ) O(d^{2.5} \sqrt{n} \log(n)) O ( d 2.5 n log ( n )) . We consider a certain hybridization construction which produces a subgroup of P U ( n , 1 ) {\rm PU}(n,1) PU ( n , 1 ) from a pair of lattices in P U ( n − 1 , 1 ) {\rm PU}(n-1,1) PU ( n − 1 , 1 ) . Among the Picard modular groups P U ( 2 , 1 , O d ) {\rm PU}(2,1,\mathcal{O}_d) PU ( 2 , 1 , O d ) , we show that the hybrid of pairs of Fuchsian subgroups P U ( 1 , 1 , O d ) {\rm PU}(1,1,\mathcal{O}_d) PU ( 1 , 1 , O d ) is a lattice when d = 1 d=1 d = 1 and $d=7…
Motivated by the task of clustering either d d d variables or d d d points into K K K groups, we investigate efficient algorithms to solve the Peng-Wei (P-W) K K K -means semi-definite programming (SDP) relaxation. The P-W SDP has been shown in the literature to have good statistical properties in a variety of settings, but rem…
Designs efficient algorithms for online and sliding window models of subspace embeddings for all p.
problem Design efficient algorithms for online and sliding window models of subspace embeddings for all p.
method Develops nearly optimal ℓ p \ell_p ℓ p subspace embeddings for all p ∈ ( 0 , ∞ ) p\in(0,\infty) p ∈ ( 0 , ∞ ) in the online coreset and sliding window models. result First nearly optimal ℓ p \ell_p ℓ p subspace embeddings for all p ∈ ( 0 , ∞ ) p\in(0,\infty) p ∈ ( 0 , ∞ ) in the online coreset and sliding window models. In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class C ⊆ { 0 , 1 } n \mathcal C \subseteq \{0, 1\}^n C ⊆ { 0 , 1 } n , introduced by Zilles et al. (2011), is a combinatorial complexity measure characterized by the worst…
Sparse OSEs achieve optimal embedding dimension of O(d).
problem Achieving optimal embedding dimension for sparse OSEs.
method Random sparsified matrix with m ≥ ( 1 + θ ) d m \geq (1+θ)d m ≥ ( 1 + θ ) d non-zeros per column. result Sparse OSEs can achieve embedding dimension m = O ( d ) m=O(d) m = O ( d ) , improving on previous m = O ( d log ( d ) ) m=O(d\log(d)) m = O ( d log ( d )) . Study on size and depth of neural networks for approximating benign functions, showing barriers and explicit results.
problem Understanding how size and depth of neural networks affect their ability to approximate benign functions.
method Analyzing ReLU networks for benign functions, proving barriers and explicit results.
result Explicit benign functions that cannot be approximated by networks of certain sizes or depths, showing barriers to size and depth separation.
A new algorithm reduces online exp-concave optimization runtime.
problem Minimizing regret in online learning with exponentially concave losses.
method LightONS, a variant of Online Newton Step (ONS), reduces runtime to O ( d 2 T + d ω T log T ) O(d^2 T + d^ω\sqrt{T \log T}) O ( d 2 T + d ω T log T ) . result Optimal regret with reduced runtime to O ( d 2 T + d ω T log T ) O(d^2 T + d^ω\sqrt{T \log T}) O ( d 2 T + d ω T log T ) . Method constructs fundamental domains for Picard modular groups.
problem Classify and understand torsion elements in Picard modular groups.
method Systematic construction of coarse fundamental domains.
result Classification of conjugacy classes of torsion elements.
Study on embedding hyperbolic 2-orbifolds in Bianchi orbifolds.
problem Embedding closed totally geodesic hyperbolic 2-orbifolds in Bianchi orbifolds.
method Analyzing Bianchi orbifolds H 3 / P S L ( 2 , O d ) \mathbb{H}^3/PSL(2,\mathcal{O}_d) H 3 / P S L ( 2 , O d ) for large d d d . result Existence of at least c d cd c d closed embedded totally geodesic hyperbolic 2-orbifolds for large d d d . The paper analyzes phase retrieval under limited samples, ensuring a benign local landscape for convergence.
problem Ensuring a benign local landscape for phase retrieval under limited samples.
method Fine-grained analysis of local landscape properties under the regime of limited samples.
result Gradient descent can converge to an o d ( 1 ) o_d(1) o d ( 1 ) -loss solution exponentially fast under certain conditions. Let O ( D ) \mathcal{O}(D) O ( D ) be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety X X X . Given a continuous toric metric ∥ ⋅ ∥ \|\cdot\| ∥ ⋅ ∥ on O ( D ) \mathcal{O}(D) O ( D ) , we define the energy at equilibrium of ( X , φ D ˉ ) (X,φ_{\bar{D}}) ( X , φ D ˉ ) where φ D ˉ φ_{\bar{D}} φ D ˉ is the weight of the metrized toric divisor $\bar{D…
We study the action of the Veech group of square-tiled surfaces of genus two on homology. This action defines the homology Veech group which is a subgroup of SL 2 ( O D ) \textrm{SL}_2(\mathcal{O}_D) SL 2 ( O D ) where O D \mathcal{O}_D O D is a quadratic order of square discriminant. Extending a result of Weitze-Schmithüsen we show that also the h…
Researchers created group presentations for specific Bianchi groups.
problem Finding explicit group presentations for certain Bianchi groups.
method Applied Macbeath's theorem to a large horoball of the Bianchi groups as discrete subgroups of H 3 \mathbf{H}^3 H 3 . result Produced a complete list of group presentations for specified Bianchi groups.
Picard modular groups are shown to be generated by complex reflections.
problem Understanding the structure of Picard modular groups using reflections.
method Using presentations from previous works to show generation by reflections.
result Picard modular groups m P U ( 2 , 1 , O d ) {
m PU}(2,1,\mathcal{O}_d) m P U ( 2 , 1 , O d ) are generated by complex reflections. We study density estimation for classes of shift-invariant distributions over R d \mathbb{R}^d R d . A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any direction. Shift-invariance relaxes smoothness assumptions commonly used in non-p…
In this paper we study the adaptive learnability of decision trees of depth at most d d d from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…
EM algorithm achieves optimal sample complexity for learning two-component mixed linear regression.
problem Learning two-component mixed linear regression under varying signal-to-noise ratios.
method Analysis of EM algorithm convergence rates under different SNR regimes.
result EM algorithm achieves minimax optimal sample complexity in all SNR regimes.
Study metric learning from limited preference comparisons, showing how low-dimensional structure can still reveal metric information.
problem Learning metric from limited pairwise preference comparisons.
method Ideal point model, divide-and-conquer approach for low-dimensional structure.
result Metric can be jointly identified even with limited comparisons when items exhibit low-dimensional structure.
Efficiently estimates Gaussian distributions privately and robustly.
problem Private and robust estimation of Gaussian distributions.
method Efficient algorithms for pure and approximate differential privacy models.
result Optimal sample complexity in both pure and approximate differential privacy settings.
New memory-query tradeoffs for convex optimization algorithms.
problem Optimizing memory usage for convex optimization algorithms.
method Analyzing randomized first-order algorithms for minimizing convex functions.
result Cutting plane methods are optimal in terms of memory and query complexity.
Memory-constrained algorithms need superlinear memory for efficient convex optimization.
problem Efficiently minimizing convex functions with limited memory.
method Analyzing first-order algorithms with superlinear memory constraints.
result Superlinear memory is necessary for optimal performance in convex optimization.
Deterministic algorithm estimates ridge regression with minimal space.
problem Estimating ridge regression solutions efficiently.
method Deterministic space-efficient algorithm using Frequent Directions.
result First o ( d 2 ) o(d^2) o ( d 2 ) space deterministic streaming algorithm with guaranteed error.