Two new regularization methods improve neural network performance and complexity control.
problem Improving neural network performance and complexity control with correlated or high-dimensional features.
method Two regularization strategies: covariance-aware ridge and covariance-aware lasso.
result Improves predictive performance and complexity control over standard penalties.
Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by providing a way to treat sequential data. However, RNNs are hard to train using con…
Unified framework for rare feature selection and aggregation in high-dimensional statistics.
problem Challenges in high-dimensional statistics due to rare features.
method Developed a unified computational framework for norms promoting discrete structures, using orthogonal projection oracle.
result Proposed estimation procedure for automatic feature selection and aggregation with statistical bounds.
Paper proposes DP-Thresholding for estimating sparse high-dimensional covariance matrices with differential privacy.
problem Estimating sparse high-dimensional covariance matrices under differential privacy constraints.
method DP-Thresholding method for achieving non-trivial error bounds.
result DP-Thresholding achieves significant error bounds compared to existing methods.
Novel method learns memory kernels in Langevin equations.
problem Estimating memory kernels in Langevin equations.
method Regularized Prony method for correlation functions, followed by regression over Sobolev norm-based loss function with RKHS regularization.
result Method outperforms other regression estimators in exponentially weighted L^2 space.
New L1 regularization controls neural network generalization error and sparsifies input dimensions.
problem Selecting the optimal number of hidden neurons in neural networks.
method Theoretical analysis of L1 regularization in two-layer neural networks. result Appropriate L1 regularization leads to near minimax optimal generalization risk bounds. Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on the kernel weights or block-norm-based regularization, which is more common in str…
New bounds for online portfolio selection without smoothness assumptions.
problem Online portfolio selection with non-Lipschitz, non-smooth losses.
method Data-dependent bounds using novel smoothness characterizations and FTRL with self-concordant regularizers.
result Achieves logarithmic regrets when data is 'easy' and sublinear worst-case regrets.
We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.
Study shows SGD's generalization is not explained by implicit bias.
problem Explaining the generalization ability of overparameterized learning algorithms.
method Revisited Stochastic Convex Optimization with SGD, demonstrating limitations of implicit bias.
result No distribution-independent or distribution-dependent implicit regularizer can explain SGD's generalization.
In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in Lp-n…
Optimal estimates derived for residual networks' generalization error.
problem Estimating the generalization error of residual networks.
method Derives optimal a priori estimates using a weighted path norm.
result Optimal error estimates are comparable to Monte Carlo error rates.
Paper introduces new risk norms based on ES with flexible distortion functions.
problem Risk quantification and anomaly detection in financial data.
method Developed generalized Expected-Shortfall (ES) norms using distortion risk measures and duality theory.
result Unified analytical framework for risk quantification and practical applications.
This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is determined by one crucial design parameter. The main contribution is a methodology to app…
Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and upper-bounds showing that the sample complexity scales with the representation di…
New methods predict neural network quality without access to training data.
problem Predicting neural network quality without access to training or testing data.
method Meta-analysis of pretrained models using norm and power law based metrics.
result Power law based metrics can better distinguish well-trained from poorly-trained models.
Network anomaly detection is still a vibrant research area. As the fast growth of network bandwidth and the tremendous traffic on the network, there arises an extremely challengeable question: How to efficiently and accurately detect the anomaly on multiple traffic? In multi-task learning, the traffic consisting of flo…
The paper offers generalization bounds for Transformers that ignore sequence length.
problem Developing generalization bounds for Transformers that are independent of sequence length.
method Covering number approach to upper bound Rademacher complexity of bounded linear transformations.
result Theoretical bounds for Transformer generalization are independent of sequence length.
In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse …
We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.
problem Analyzing coresets for regularized regression problems.
method Examined coresets for ridge regression and proposed a modified lasso problem.
result No coreset for regularized regression can be smaller than the unregularized version when reqs. Unified PAC-Bayesian framework for deep learning generalization.
problem Limitations of existing PAC-Bayesian norm-based bounds for deep neural networks.
method Unified framework using anisotropic Gaussian posteriors and sensitivity matrix.
result Comparable or tighter generalization bounds compared to state-of-the-art approaches.
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framewor…
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…
Extends importance sampling to nonlinear models using adjoint operators.
problem Lack of tools for identifying important data points in nonlinear models.
method Introduces adjoint operator for nonlinear maps, generalizes norm and leverage scores.
result Generalized scores provide approximation guarantees for nonlinear mappings.
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., ℓ1 optimization and SPICE, with an infinitely dense grid…
The paper provides statistical guarantees for sparse deep learning.
problem Understanding the potential and limitations of sparse deep learning.
method Develops statistical guarantees for different types of sparsity in sparse deep learning.
result Statistical guarantees for sparse deep learning with mild dependence on network widths and depths.
Study analyzes adversarial training dynamics without data distribution assumptions.
problem Understanding training dynamics of adversarial training without data distribution assumptions.
method Mean field theory approach to analyze adversarial training in random deep neural networks.
result Upper bounds of adversarial loss derived empirically and theoretically.
A toolkit for path-norms enhances neural network generalization bounds.
problem Establishing generalization bounds for modern neural networks.
method Introducing a comprehensive toolkit for path-norms in ReLU networks with various operations.
result Established generalization bounds for modern neural networks that are the most widely applicable and recover/beat the sharpest known bounds.
U-Clip clips gradients to reduce bias without discarding them.
problem Reduces bias in stochastic gradient descent.
method Maintains a buffer of clipped gradients to add to next iteration.
result U-Clip updates are unbiased on average.
This study extends verifiable learning to boosted tree ensembles, enabling efficient security verification.
problem Efficiently verifying the robustness of boosted tree ensembles against norm-based attackers.
method Formal verification of robustness for large-spread boosted tree ensembles, considering L∞-norm and pseudo-polynomial time for Lp-norm verification. result Polynomial time verification for L∞-norm attackers, NP-hard for other norms, and pseudo-polynomial time for Lp-norm verification. Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
This paper explores how the generalization of substitute classifiers affects the success of black-box adversarial attacks.
problem Understanding the factors driving the transferability of black-box adversarial examples.
method Max-min adversarial example game framework and theoretical generalization bounds.
result Substitute NN with better generalization behavior results in more transferable adversarial examples.
The smart grid vision entails advanced information technology and data analytics to enhance the efficiency, sustainability, and economics of the power grid infrastructure. Aligned to this end, modern statistical learning tools are leveraged here for electricity market inference. Day-ahead price forecasting is cast as a…
New study shows how model complexity affects test risk, challenging classical theory.
problem Understanding how test risk scales with model complexity for large over-parametrized deep networks.
method Developed norm-based capacity measures for random features based estimators, providing precise characterization of estimator's norm concentration and test error.
result Predicted learning curve shows a phase transition from under- to over-parameterization, confirming classical U-shaped behavior with appropriate capacity measures.
CNN layers with large norms are still robust to adversarial attacks.
problem Understanding the relationship between layer norms and adversarial robustness in CNNs.
method Theoretical analysis of ℓ1 and ℓ∞ norms, norm decay method, adversarial training frameworks. result Adversarially robust CNNs can have comparable or larger layer norms than non-adversarially robust ones.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: (i) \emph{leverage scores-based} and (ii) \emph{norm-based} feature selection. Experimenta…
Improved robustness for high-dimensional Kalman filtering.
problem Convergence issues in sequential variational inference filter (VIF).
method Variational Kalman Filtering with Hinf-based correction.
result Improved feasibility and robustness in high-dimensional systems.
New bounds adaptively control spectral complexity of trained Transformers.
problem Understanding why Transformers generalize well in machine learning.
method Spectrum-adaptive post hoc generalization bounds for multi-layer Transformers.
result Bounds adaptively trade off spectral complexity against dimension and depth factors.
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
Estimates latent norms and Gram matrices for graphs on Euclidean balls.
problem Estimating latent points and their relationships in graphs on Euclidean balls.
method Estimates latent norms and Gram matrices using observed graph data.
result Graphs on Euclidean balls can have power-law degree distributions.
COMRADE is a communication-efficient, Byzantine-resilient second-order optimization algorithm.
problem Byzantine failures in distributed optimization.
method COMRADE is a communication-efficient, second-order optimization algorithm that uses a simple norm-based thresholding rule to filter out Byzantine workers.
result COMRADE achieves linear-quadratic convergence and is robust against Byzantine workers.
Improved generalization bounds for multi-class CNNs without explicit class dependence.
problem Generalization error bounds for deep learning with multi-class CNNs.
method Adapted Rademacher analysis to incorporate weight sharing, reducing dependence on the number of classes.
result Bounds have no explicit dependence on the number of classes, scaling with the norm of weight matrices.
New scaling laws explain deep learning performance growth.
problem Understanding neural network performance growth.
method Analyzed entire training dynamics of various architectures.
result Identified two dynamical scaling laws.
Semantify-NN verifies neural network robustness against semantic perturbations.
problem Verifying robustness of neural networks against semantic adversarial attacks.
method Inserting semantic perturbation layers (SP-layers) into neural networks to verify robustness.
result Semantify-NN significantly improves robustness verification performance over ℓp-norm-based methods. In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices an…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…