Study uncovers new phase transitions in asymmetric causal inference scenarios.
problem Understanding typical phase transitions in asymmetric causal inference.
method Combining Causal inference (C-inf) and Low-rank recovery (LRR) with Random duality - Free probability theory (RDT-FPT).
result Discovering a doubling low-rankness phenomenon in asymmetric scenarios.
Gradient descent solves asymmetric low-rank matrix factorization efficiently.
problem Optimizing asymmetric low-rank matrix factorization with non-convex and non-smoothness issues.
method Randomly initialized gradient descent with new symmetrization and perturbation techniques.
result Gradient descent converges to a global minimum of the asymmetric low-rank factorization problem.
Gradient descent solves asymmetric low-rank matrix sensing without balancing.
problem Recovering asymmetric low-rank matrices from linear measurements.
method Gradient descent with spectral initialization, avoiding balancing term.
result Gradient descent converges linearly without balancing, factors stay balanced.
Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.
problem Reconstructing asymmetric low-rank matrices from linear measurements.
method Factorized gradient descent with coupling and regularization properties.
result Gradient descent from small random initialization converges to globally optimal and generalizing solutions.
Low-rank factorization is a standard way to make structured optimization problems in machine learning more tractable by replacing matrix variables with compact factors. For positive semidefinite (PSD) variables, the symmetric Burer--Monteiro factorization (sBMF) writes Z=XX⊤ with a single low-rank factor X. A r…
Paper analyzes asymmetry in LoRA initialization for foundation models.
problem Asymmetry in LoRA initialization affects generalization of foundation models.
method Theoretical analysis of asymmetric LoRA with frozen random factors.
result Upper bound on sample complexity of $ ilde{\mathcal{O}}\left(\frac{\sqrt{r}}{\sqrt{N}}
ight)$ with high probability.
In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) …
Gradient descent recovers principal components of overparametrized asymmetric matrices without explicit regularization.
problem Asymmetric matrix factorization under overparametrization with minimal rank assumptions.
method Vanilla gradient descent with small random initialization and proper early stopping.
result Gradient descent produces the best low-rank approximation without explicit regularization.
Paper tackles robust matrix completion with heavy-tailed noise.
problem Estimating a low-rank matrix from noisy incomplete data.
method Adaptive Huber loss for robustness, nonconvex algorithm with spectral initialization.
result Achieves minimax-optimal statistical estimation error under bounded second moment condition.
SKI speeds up Toeplitz Neural Networks by avoiding explicit decay bias and using frequency response.
problem Efficiently compute and update Toeplitz matrices in neural networks.
method Sparse plus low-rank decomposition, asymmetric SKI, frequency response modeling.
result Achieved significant speedup with minimal performance loss.
We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We rigorously prove that gradient flow (i.e. gradient descent with infinitesimal step …
Extends MMF to nonsymmetric matrices for hierarchical structure.
problem Capturing hierarchical structure in nonsymmetric matrices.
method Multiresolution Matrix Factorization (MMF) extended to nonsymmetric matrices.
result Effective for matrix compression tasks, outperforming low-rank methods.
Study analyzes accuracy of tensor deflation in noisy conditions.
problem Analyzing accuracy of tensor deflation in noisy conditions.
method Asymptotic study of Hotelling-type tensor deflation in large tensor dimensions.
result Characterization of estimated singular values and singular vector alignments.
New algorithm completes noisy tensors quickly and accurately.
problem Reconstructing low-rank tensors from incomplete and noisy data.
method Two-stage nonconvex gradient descent algorithm.
result Achieves near-optimal statistical guarantees and linear time complexity.
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix M⋆∈Rn×n, yet only a randomly perturbed version M is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\s…
Sharp global guarantees for noisy overparameterized low-rank recovery.
problem Understanding practical success of overparameterization in noisy conditions.
method Unified proof technique combining escape directions and counterexample inexistence.
result Near-second-order points achieve minimax-optimal recovery bounds.
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic acc…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…
APGD algorithm reconstructs point set from partial distance measurements.
problem Reconstructing point set configuration from partial Euclidean distance measurements.
method Asymmetric Projected Gradient Descent (APGD) for EDMC problem.
result Global convergence and exact recovery with O(μ2r3κ2nlogn) observations. Many computer vision tasks involve processing large amounts of data contaminated by outliers, which need to be detected and rejected. While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guar…
Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.
problem Analysis of geometric properties on asymmetric metric measure spaces.
method Introduction of upper gradients, q-Laplacian, and q-heat flow in asymmetric settings. result Extension of concepts from symmetric to asymmetric metric measure spaces.
The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.
problem Matrix sensing problem with over-parameterized gradient descent.
method Analyzes symmetric and asymmetric parameterizations, provides lower bounds and convergence rates.
result Over-parameterization slows down GD convergence, but asymmetric parameterization can speed up convergence.
A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.
problem Inadequate handling of asymmetric error distributions in adaptive filtering.
method Proposes asymmetric correntropy using an asymmetric Gaussian kernel and develops a robust adaptive filtering algorithm.
result The proposed algorithm shows better steady-state convergence performance for asymmetric error distributions.
New metrics for Anosov representations defined from Thurston's asymmetric metrics.
problem Defining metrics for Anosov representations.
method Generalizing Thurston's asymmetric metric to Anosov representations.
result Provides a (possibly asymmetric) Finsler distance in some cases.
Generalizes Thurston's asymmetric metric to flat metrics.
problem Defining an asymmetric metric on flat metrics.
method Defined an asymmetric metric on the space of unit-area flat metrics.
result Discussed two different topologies from the asymmetry.
This study examines asymmetric cross-correlations in cryptocurrency markets using fractal analysis.
problem Exploring asymmetric multifractal cross-correlations in cryptocurrency markets.
method Fractal analysis and MF-ADCCA method to investigate asymmetric volatility dynamics.
result Cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH.
Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
problem Lack of precise theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
method Adapting a finite-time convergence analysis to the asymmetric actor-critic setting with linear function approximators.
result A finite-time bound reveals that the asymmetric critic eliminates aliasing errors in the agent state.
This work presents deep asymmetric networks with a set of node-wise variant activation functions. The nodes' sensitivities are affected by activation function selections such that the nodes with smaller indices become increasingly more sensitive. As a result, features learned by the nodes are sorted by the node indices…
Low-rank matrix factorization (LRMF) has received much popularity owing to its successful applications in both computer vision and data mining. By assuming noise to come from a Gaussian, Laplace or mixture of Gaussian distributions, significant efforts have been made on optimizing the (weighted) L1 or L2-norm los…
We consider the problem of designing locality sensitive hashes (LSH) for inner product similarity, and of the power of asymmetric hashes in this context. Shrivastava and Li argue that there is no symmetric LSH for the problem and propose an asymmetric LSH based on different mappings for query and database points. Howev…
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
The paper improves asymmetric causality tests by addressing inefficiencies and statistical significance issues.
problem Inefficiencies and statistical significance issues in asymmetric causality tests.
method Improved asymmetric causality tests via partial cumulative sums for positive and negative components, explicitly testing differences between causal parameters.
result Efficiently tested hypotheses on asymmetric causal interaction between financial markets.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
We propose Deep Asymmetric Multitask Feature Learning (Deep-AMTFL) which can learn deep representations shared across multiple tasks while effectively preventing negative transfer that may happen in the feature sharing process. Specifically, we introduce an asymmetric autoencoder term that allows reliable predictors fo…
Study of classification in asymmetric quasi-metric spaces.
problem Classification in asymmetric quasi-metric spaces.
method Sample compression and nearest neighbor algorithm.
result Algorithm has favorable statistical properties.
In this paper we show how the study of asymmetric R&D alliances, that are those between young and small firms and large and MNEs firms for knowledge exploration and/or exploitation, requires the adoption of a coopetitive framework which consider both collaboration and competition. We draw upon the literature on asymmet…
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
problem Phase transitions in singular values and vectors of large random matrices.
method Analysis of singular values and vectors of long rectangular random matrices, and tensor unfolding algorithm for asymmetric rank-one spiked tensor models.
result An exact threshold for tensor unfolding to detect signals, independent of unfolding procedure.
Bayesian VI copula models capture asymmetric intraday equity dependence.
problem Modeling asymmetric and extreme tail dependence in financial data.
method Bayesian variational inference for skew-t copula models in high dimensions.
result The copula captures substantial heterogeneity in asymmetric dependence over equity pairs and time.
This work describes compactifications of metric spaces and vector spaces using asymmetric norms.
problem Compactifying metric spaces and vector spaces using asymmetric norms.
method Nonstandard methods, ultrapowers of the spaces at hand.
result Polyhedral compactifications of vector spaces with stratified structure.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
Extends metric to Margulis spacetimes for convex properties.
problem No specific problem stated; extends metric.
method Extends Thurston's asymmetric metric to Margulis spacetimes and proves convex properties.
result Established convex properties of the extended metric.
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to create generalized asymmetric versions of the Laplace and normal distributions, whic…
Enhances reinforcement learning with partial state information.
problem Improving learning under partial observability with limited privileged signals.
method Introduced informed asymmetric actor-critic framework that uses arbitrary state-dependent privileged signals.
result Unbiased policy gradient estimates with arbitrary privileged signals.
This paper studies gradient flows in asymmetric metric spaces and proves existence results.
problem Investigating gradient flows in asymmetric metric spaces.
method Discrete approximation and natural convexity assumption on potential function.
result Existence of curves of maximal slope in asymmetric metric spaces.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
Proposes a new OAL algorithm for imbalanced data with limited labels.
problem Handling imbalanced unlabeled datastream with limited query budget.
method Integrates asymmetric losses and queries strategies, uses second-order optimization, and applies sketching technique.
result Demonstrates improved performance and efficiency in class imbalance.
Modified asymmetric hidden Markov models for time series with autoregressive components.
problem Dynamic relationships between variables in time series data.
method Introducing an asymmetric autoregressive component to recent asymmetric hidden Markov models.
result The model can choose the optimal autoregressive order for better likelihood.