RER improves sample complexity by updating in reverse order.
problem Theoretical analysis limits RER's convergence rate.
method Tighter analysis for larger learning rates and longer sequences.
result RER converges faster with larger learning rates and longer sequences.
A new method for tighter privacy loss accounting in adaptive analyses.
problem Ensuring individual privacy in adaptive analyses while staying within a privacy budget.
method A personalized privacy loss estimate and a Rényi differential privacy filter.
result Personalized privacy loss accounting can be practical and tighter than existing methods.
Improved spectral clustering with fewer eigenvectors performs better.
problem Improving spectral clustering performance under weaker conditions.
method Tighter analysis and using fewer eigenvectors for embedding.
result Spectral clustering can produce better results with fewer eigenvectors.
This paper improves Bayesian optimization methods with tighter regret bounds and practical solutions.
problem Improving Bayesian optimization methods with tighter regret bounds and practical solutions.
method The paper analyzes and compares different acquisition functions (GP-UCB, TS, PIMS) to achieve tighter Bayesian cumulative regret bounds and address practical issues.
result PIMS achieves the tighter BCR bound and avoids hyperparameter tuning, unlike GP-UCB and TS.
FedExProx's performance is no better than GD for quadratic optimization.
problem Improving convergence of parallel proximal algorithms.
method Developed a novel analysis framework to establish tighter convergence rates.
result FedExProx can outperform GD in non-strongly convex quadratic problems.
Paper simplifies calculating causation probabilities and ranks root causes.
problem Computational challenges in assessing causal relationships.
method Algorithmic simplifications and novel methodological framework for Root Cause Analysis.
result Significantly reduces computational complexity for calculating causation probabilities.
This paper provides a theoretical analysis of domain adaptation based on the PAC-Bayesian theory. We propose an improvement of the previous domain adaptation bound obtained by Germain et al. in two ways. We first give another generalization bound tighter and easier to interpret. Moreover, we provide a new analysis of t…
New bound for neural networks with full-rank weights, independent of network width.
problem Understanding generalization of neural networks with full-rank weight matrices.
method Using Koopman operators to derive a tighter generalization bound for full-rank weight matrices.
result The bound is tighter than existing norm-based bounds when condition numbers are small.
Paper improves neural network robustness analysis for safety-critical systems.
problem Uncertainty in neural network outputs for safety-critical systems.
method Unified propagation and partition approaches to provide tighter bounds.
result Proposed algorithms give tighter bounds than existing methods for the same computation time.
We study the risk performance of distributed learning for the regularization empirical risk minimization with fast convergence rate, substantially improving the error analysis of the existing divide-and-conquer based distributed learning. An interesting theoretical finding is that the larger the diversity of each local…
Strong worst-case performance bounds for episodic reinforcement learning exist but fortunately in practice RL algorithms perform much better than such bounds would predict. Algorithms and theory that provide strong problem-dependent bounds could help illuminate the key features of what makes a RL problem hard and reduc…
Unified SGD method improves convergence for nested optimization problems.
problem Stochastic nested optimization problems.
method ALTERNATE dESCEN (ALSET) method leveraging hidden smoothness.
result Requires O ( ε − 2 ) {\cal O}(ε^{-2}) O ( ε − 2 ) samples to achieve an ε ε ε -stationary point. New analysis improves generalization bounds for meta-learning.
problem Improving generalization in meta-learning algorithms.
method Information-theoretic analysis of MAML and its stochastic variant.
result Data-dependent generalization bound is tighter and non-vacuous.
Improved generalization bounds for SGD in non-convex learning.
problem Understanding generalization properties of SGD in non-convex settings.
method Introducing Type II perturbed SGD (T2pm-SGD) to analyze generalization error bounds.
result Tighter generalization error bounds for SGD in non-convex learning, especially for sub-Gaussian and bounded loss functions.
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…
Improved DP algorithms for non-convex optimization with tighter generalization bounds.
problem Private stochastic non-convex optimization in high-dimensional spaces.
method Differential privacy techniques, including adaptive algorithms like DP RMSProp and DP Adam, combined with adaptive data analysis.
result Achieved a sharper rate of p 4 / n \sqrt[4]{p}/\sqrt{n} 4 p / n for population loss, improving upon previous bounds. Gen-CUDE is a neural network for denoising noisy channels.
problem Denoising in finite-input, general-output noisy channels.
method Unsupervised neural network trained on noisy data.
result Gen-CUDE achieves better denoising results than other methods.
Paper improves robustness of GNNs against adversarial attacks.
problem Understanding robust generalization of GNNs in adversarial settings.
method Develops a sensitivity-aware PAC-Bayesian framework for MPGNNs.
result Derives tighter robust generalization bounds for MPGNNs.
A new method to measure neural network expressiveness using tighter upper bounds.
problem Measuring the expressiveness of deep neural networks (DNNs).
method Proposes a new tighter upper bound for the number of linear regions in rectifier networks, using matrix computation.
result The proposed upper bound is tighter than existing ones and explains the performance improvements of skip connections and residual structures.
Improved PAC-Bayesian bounds by considering example difficulty.
problem Improving generalization bounds in machine learning.
method Introducing a modified excess risk that leverages example difficulty to reduce variance and tighten PAC-Bayesian bounds.
result Tighter PAC-Bayesian generalization bounds for machine learning models.
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
New tighter bounds for learning algorithms from Steinke & Zakynthinou's supersample setting.
problem Improving generalization bounds for machine learning algorithms.
method Information-theoretic approach using projected loss and Rademacher sequence.
result The new bounds are tighter than previous information-theoretic bounds.
Debona improves neural network verification by faster and tighter bounds.
problem Proving adversarial robustness of neural networks is computationally hard.
method Decouples upper and lower bounds computation, re-implements Neurify.
result 94% reduction in runtime for proving robustness of max-pooling layers.
New insights into using momentum for non-convex optimization.
problem Improving training of non-convex models like deep neural networks.
method Developed a Lyapunov analysis of SGD with momentum using stochastic primal averaging.
result Precise conditions under which SGD+M outperforms SGD and optimal hyper-parameter schedules.
Private ALS method improves matrix completion with tighter rates and better privacy.
problem Differential privacy in matrix completion for user-level privacy.
method Joint differentially private ALS method with tighter sample complexity and privacy trade-offs.
result Achieves nearly optimal sample complexity and best privacy/utility trade-off.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better vari…
New methods improve gradient estimation in autoencoders, enhancing generative network performance.
problem Improving gradient estimation in autoencoders to enhance learning.
method Developed and studied three methods: PIWAE, MIWAE, CIWAE.
result Generated approximate posterior distributions closer to true posterior distribution.
Novel analysis improves weighted majority vote in multiclass classification.
problem Improving the performance of weighted majority vote in multiclass classification.
method Analyzes expected risk of weighted majority vote, considering prediction correlations and provides a bound for efficient minimization.
result Minimization of the new bound typically does not degrade the test error of the ensemble.
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…
We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use our tighter representation to derive a general f-divergence estimator based on t…
Ahpatron improves online kernel learning with tighter mistake bounds.
problem Improving mistake bounds in online kernel learning with budget constraints.
method Introducing Ahpatron, a new model that uses an aggressive updating rule and a budget maintenance mechanism to approximate AVP.
result Ahpatron achieves tighter mistake bounds compared to previous models.
Improved robustness for deep neural networks with tighter bounds and attacks.
problem Loose upper bounds and prohibitive computation in existing adversarial robustness methods.
method Primal approach with exact Lipschitz certificates for ReLU networks and modern architectures, and novel Wasserstein Distributional Attacks.
result Tighter upper bounds and greater flexibility in attack points compared to existing methods.
New analysis shows halting time is predictable for large models, improving optimization efficiency.
problem Understanding the average-case complexity of optimization algorithms for large-scale models.
method Average-case analysis of first-order methods on random least squares and neural networks.
result Halting time is independent of input distribution, leading to tighter convergence rates.
Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.
problem Analyzing convergence of hyperparameters in game optimization.
method Frequency-domain framework using High-Resolution Differential Equations (HRDEs) and Laplace transforms.
result Derives precise convergence criteria for the Lookahead algorithm.
Study on the probability of immunity and its bounds.
problem Estimating the probability of immunity and its bounds.
method Derive necessary and sufficient conditions for non-immunity and ε-bounded immunity; introduce indirect immunity; propose sensitivity analysis.
result Estimate the probability of benefit and produce tighter bounds of the probability of benefit.
We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning. We provide an improved convergence analysis of SVRPG and show that it can find an ε ε ε -approximate stationary point of the performance function within O ( 1 / ε 5 / 3 ) O(1/ε^{5/3}) O ( 1/ ε 5/3 ) trajectories. This s…
A method to assess sensitivity to unmeasured confounding with sharp bounds.
problem Assessing the impact of unmeasured confounding on causal effects.
method Sets two intuitive parameters to estimate sensitivity intervals.
result Bounds on true causal effects can be tighter than existing methods.
New model-free algorithm achieves similar LQR regret guarantees.
problem Model-free control of linear dynamical systems under quadratic costs.
method Online policy gradient scheme with policy space cost analysis.
result Achieves regret scaling with √T, matching model-based methods.
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
Stress shocks are often calculated as multiples of the standard deviation of a history set. This paper investigates how many standard deviations are required to guarantee that this shock exceeds any observation within the history set, given the additional constraint of kurtosis. The results of this analysis are then us…
We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our boun…
Improves privacy amplification by shuffling for differential privacy.
problem Enhancing privacy guarantees in systems with anonymous data contributions.
method Theoretical and numerical analysis of Rényi differential privacy parameters and privacy amplification by shuffling.
result First asymptotically optimal analysis of Rényi differential privacy parameters for shuffled outputs.
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
Paper improves neural network robustness certification with tighter radii estimates.
problem Certifying neural networks' robustness against adversarial attacks.
method Advanced algorithms for discrete and continuous domains, optimizing sample size, standard deviation, and temperature.
result Significant improvement in certified test-set accuracy with tighter certified radii bounds.
New analysis explains pathology of deep Gaussian processes.
problem Pathology of deep Gaussian processes reduces learning capacities with increased layers.
method Study nonlinear dynamic systems corresponding to DGPs, derive recurrence relations.
result Provide tighter bounds and rate of convergence for dynamic systems.