We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher…
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48 results for “transductive PAC-Bayesian”
The paper establishes bounds for transductive learning using information theory.
problem Transductive learning generalization gap control.
method Information theory, PAC-Bayes, mutual information, conditional mutual information, different information measures.
result Established transductive information-theoretic and PAC-Bayesian bounds.
FLowDUP trains personalized models with unlabeled clients in low dimensions.
problem Training personalized models on clients with only unlabeled data.
method FLowDUP uses a forward pass with unlabeled data and a transductive PAC-Bayesian bound to generate personalized models in a low-dimensional subspace.
result FLowDUP enables efficient communication and computation with personalized models generated from unlabeled data.
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
This research improves PAC-Bayesian bounds for classification tasks using convexified loss.
problem Deriving generalization bounds for classification tasks with non-convex loss functions.
method Shift focus to misclassification excess risk bounds for PAC-Bayesian classification using convex surrogate loss and leveraging PAC-Bayesian relative bounds in expectation.
result Improved PAC-Bayesian bounds for classification tasks with convex surrogate loss.
New PAC-Bayesian bounds for multi-view learning using Rényi divergence.
problem Applying PAC-Bayesian theory to multi-view learning.
method Introducing novel PAC-Bayesian bounds based on Rényi divergence for multi-view learning.
result Efficient optimization algorithms that align with theoretical bounds.
Local regularization fails in transductive learning for some multiclass problems.
problem Whether local regularization can learn all transductive multiclass problems.
method Provided a negative answer by exhibiting a specific multiclass problem.
result Local regularization cannot learn all transductive multiclass problems.
New algorithms minimize PAC-Bayesian C-Bound for majority voting, leading to scalable and accurate predictors.
problem Improving majority vote classifiers using PAC-Bayesian bounds.
method Directly optimizing PAC-Bayesian guarantees on the C-Bound with gradient descent.
result Self-bounding majority vote learning algorithms with scalable and accurate predictors.
PAC-Bayesian bounds for stochastic LTI systems derived.
problem Error bounds for stochastic LTI systems.
method PAC-Bayesian theory applied to autonomous stochastic LTI models.
result Error bounds for stochastic LTI systems derived.
New PAC-Bayesian bounds for online learning with data streams.
problem Challenges of traditional PAC-Bayesian bounds in dynamic data collection.
method Developed new PAC-Bayesian bounds in online learning framework, using updated regret definition and batch-to-online conversion.
result PAC-Bayesian bounds hold for online learning with dependent data and non-convex losses.
Wide stochastic networks show Gaussian behavior and improve training with PAC-Bayesian methods.
problem Analyzing and training over-parameterised neural networks with large width.
method Establishing Gaussian behavior for a stochastic architecture, applying PAC-Bayesian training.
result PAC-Bayesian training on large but finite-width networks outperforms standard methods.
New PAC-Bayesian bounds improve Sliced-Wasserstein distances.
problem Improving statistical properties of Sliced-Wasserstein distances.
method Leveraging PAC-Bayesian theory to provide bounds and learning procedures.
result PAC-Bayesian generalization bounds for adaptive SW distances.
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This …
This work provides statistical guarantees for VAEs using PAC-Bayesian theory.
problem Theoretical properties of VAEs remain open questions.
method PAC-Bayesian theory to derive statistical guarantees.
result Upper bounds on Wasserstein distance between input and generative model.
New PAC-Bayesian bounds provide practical guarantees for neural networks.
problem Loose derandomization step in PAC-Bayesian bounds for deterministic models.
method Introduce disintegrated PAC-Bayesian bounds for deterministic models.
result Significant practical improvement over state-of-the-art bounds.
Proved a combinatorial conjecture in machine learning.
problem None explicitly stated in the abstract.
method Binomial and multinomial sums identities.
result Proved a combinatorial conjecture.
Improved mistake bounds for transductive online learning.
problem Quantifying the power of unlabeled data in online learning.
method Proving lower and upper bounds on transductive mistake bounds.
result Exponential improvement in mistake bounds for transductive learning.
New method TLC improves transductive learning bounds.
problem Sharp generalization bounds for transductive learning.
method Transductive Local Complexity (TLC) framework.
result Nearly sharp bounds consistent with inductive results.
Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and deterministic predictors often performs well in practice. To fill this gap, we develop…
Transductive learning considers situations when a learner observes labelled training points and unlabelled test points with the final goal of giving correct answers for the test points. This paper introduces a new complexity measure for transductive learning called Permutational Rademacher Complexity (PRC) and …
PAC-Bayesian theory applied to data-dependent hypothesis sets yields uniform generalization bounds.
problem Proving uniform generalization bounds for data-dependent hypothesis sets.
method Applying PAC-Bayesian framework on 'random sets' and considering data-dependent hypothesis sets.
result Data-dependent uniform generalization bounds are proven, providing tighter and unified results.
This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the se…
The paper finds a fundamental trade-off between confidence and efficiency in transductive conformal prediction.
problem The challenge is to balance confidence and efficiency in predicting multiple data points.
method The authors derive a strict finite-sample bound and introduce a practical algorithm to approach this bound.
result Any non-trivial confidence level leads to exponential growth in prediction set size, with a linear scaling in the number of samples.
Transductive learning considers a training set of labeled samples and a test set of unlabeled samples, with the goal of best labeling that particular test set. Conversely, inductive learning considers a training set of labeled samples drawn iid from , with the goal of best labeling any future sample…
The study examines how equivariance in networks affects generalization error using PAC-Bayesian bounds.
problem Understanding how equivariance in networks impacts generalization error.
method Utilized PAC-Bayesian analysis for equivariant networks, deriving norm-based bounds for generalization error.
result The bound indicates that using larger group size in the model improves generalization error.
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanatio…
Extractive compression is a challenging natural language processing problem. This work contributes by formulating neural extractive compression as a parse tree transduction problem, rather than a sequence transduction task. Motivated by this, we introduce a deep neural model for learning structure-to-substructure tree …
Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.
problem Characterizing predictive power of LTI systems learned from data.
method PAC-Bayesian bounds for LTI stochastic dynamical systems with inputs.
result Finite-sample error bounds for learning algorithms of LTI systems.
Paper introduces new PAC-Bayesian bounds for multi-view domain adaptation.
problem Lack of attention to multi-view learning in domain adaptation.
method Adapted distance measure for multi-view domain adaptation using Pac-Bayesian theory.
result Introduced novel Pac-Bayesian bounds for multi-view domain adaptation.
Adversarial robust learning improved for transductive setting.
problem Adversarial robust learning in transductive setting.
method Simple transductive learner for bounded VC dimension classes.
result Robust error rate linear in VC dimension, adaptive to perturbation complexity.
PAC-Bayesian matrix completion with a spectral scaled Student prior offers efficient inference.
problem Matrix completion with underlying low-rank structure.
method Spectral scaled Student prior and PAC-Bayesian bounds.
result Minimax-optimal oracle inequality for model misspecification and general sampling distribution.
The study improves PAC-Bayesian bounds for adversarial generative models.
problem Improving generalization bounds for adversarial generative models.
method Extending PAC-Bayesian theory to generative models, developing bounds for Wasserstein and total variation distances.
result New training objectives for Wasserstein and Energy-Based GANs.
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …
Proposes a framework for compositional generalization in language models.
problem Lack of compositional generalization in neural networks compared to humans.
method Introduces Generalized Grammar Rules (GGRs) for transduction tasks, formalizing symmetry-based constraints.
result Framework enables models to generalize compositionally, similar to human learning.
PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelsstat.ML
Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
Many machine learning tasks can be expressed as the transformation---or \emph{transduction}---of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to name but a few. One of the key challenges in sequence transduction is learning to …
Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.
PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution . Unfortunately, most of the available bounds …
Multi-group learners suffer a penalty in transductive learning.
problem The penalty on multi-group learners in transductive learning.
method Analyzing the relationship between the number of groups and the error rate.
result The penalty can increase linearly with the number of groups, up to the square-root of the sample size.
Study shows transductive learning is equivalent to PAC learning for most natural loss functions.
problem Understanding the relationship between transductive and PAC learning models.
method Extending existing results and developing new techniques to analyze the equivalence of the two models.
result Transductive learning is essentially equivalent to PAC learning for realizable learning with most natural loss functions.
Unified framework for deriving generalization bounds in supervised learning.
problem Generalization error bounds in supervised learning.
method Data Processing Inequality PAC-Bayesian framework.
result Unified bounds on binary Kullback-Leibler generalization gap for various divergences.
PAC-Bayesian bounds improve understanding of K-NN classifier performance.
problem Improving the understanding of K-NN classifier's generalization error.
method PAC-Bayesian analysis applied to K-NN classifier in kernel space.
result PAC-Bayesian bounds provide a function of the number of redundant training examples.
New PAC-Bayesian bounds explain few-shot learning performance gaps.
problem Gap between PAC-Bayesian theory and practice in few-shot learning.
method Developed new PAC-Bayesian bounds for few-shot learning, derived MAML and Reptile from these bounds, and introduced a new PACMAML algorithm.
result PAC-Bayesian bounds explain performance of MAML and Reptile, and outperform existing algorithms.
We propose an extensive analysis of the behavior of majority votes in binary classification. In particular, we introduce a risk bound for majority votes, called the C-bound, that takes into account the average quality of the voters and their average disagreement. We also propose an extensive PAC-Bayesian analysis that …
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.
The paper surveys recent extensions of the Long-Short Term Memory networks to handle tree structures from the perspective of learning non-trivial forms of isomorph structured transductions. It provides a discussion of modern TreeLSTM models, showing the effect of the bias induced by the direction of tree processing. An…
PAC-Bayesian bounds estimate adversarial robustness.
problem Estimating robustness to imperceptible input perturbations.
method PAC-Bayesian framework for averaging over hypotheses.
result General bounds valid for any type of adversarial attacks.
Proposes a transductive matrix completion method with calibration for multi-task learning.
problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.