Study computable multiclass learning within PAC framework.
problem Computable multiclass learnability in finite label space.
method Proposed computable version of Natarajan dimension and generalized to distinguishers.
result Characterizes CPAC learnability for certain dimensions and embeddings.
Study shows realizable learnability doesn't imply agnostic learnability for distributions.
problem Learnability and robustness of distribution classes.
method Analyzes the relationship between learnability and robustness for distribution learning.
result Realizable learnability does not imply agnostic learnability for distributions.
The paper solves open questions in computable PAC learning, providing a complete landscape.
problem Understanding the boundaries and capabilities of computable PAC learning.
method Analyzing and constructing decidable hypothesis classes with different sample complexities and Littlestone dimensions.
result A complete understanding of CPAC learnability, answering open questions and confirming conjectures.
We study the question of learning an adversarially robust predictor. We show that any hypothesis class H with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes H with finite VC…
Study robust regression learning under adversarial attacks.
problem Understanding which function classes are learnable in the presence of adversarial attacks.
method Introduced a novel agnostic sample compression scheme and used fat-shattering dimension to construct adversarially robust sample compression schemes.
result Finite fat-shattering dimension classes are learnable in both realizable and agnostic settings.
This work characterizes when a hypothesis class can be k-list learned.
problem Characterizing when a hypothesis class can be k-list learned.
method Introducing the k-DS dimension and proving the equivalence of k-list learnability and the finiteness of the k-DS dimension.
result A hypothesis class is k-list learnable if and only if the k-DS dimension is finite.
The paper explores how machine learning models can be learnable despite label shifts.
problem Learnability of binary classification models in the presence of label shifts.
method Developed a performative empirical risk function that is an unbiased estimate of the true risk on the shifted distribution.
result PAC-learnable hypothesis spaces remain PAC-learnable for performative scenarios.
New insights into Valiant's learnability model reveal classes learnable with membership queries.
problem Which classes are learnable in Valiant's original model?
method Characterization using poly-size adaptive query-compression schemes and techniques for arbitrary domains.
result Learnability in Valiant's model is sandwiched between PAC and query-less variants, with halfspaces learnable with queries.
PAC-Bayes framework fails on simple 1D linear classification task.
problem Proving the learnability of simple 1D linear classification tasks using PAC-Bayes bounds.
method Demonstrated a specific 1D linear classification task that PAC-Bayes cannot analyze.
result PAC-Bayes framework cannot prove learnability of simple 1D linear classification tasks.
Investigates principles of generalization in list learning, refutes sample compression conjecture.
problem Determining applicability of classical principles in list PAC learning.
method Examines uniform convergence and sample compression in list PAC learning.
result Sample compression fails in list PAC learning, refutes conjecture.
We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not de…
Characterizes statistical complexity of realizable regression in PAC and online learning.
problem Understanding the statistical complexity of realizable regression in both PAC and online learning settings.
method Introduces minimax instance optimal learners, novel and combinatorial dimensions to characterize learnability.
result Characterizes which classes of real-valued predictors are learnable and provides necessary conditions for learnability.
New learning rule for quantum measurement classes overcomes uniform convergence issues.
problem Characterizing learnability of POVM hypothesis classes in quantum settings.
method Introduced a new learning rule called denoised ERM to address uniform convergence issues.
result Characterized learnability conditions and sample complexity bounds for POVM classes.
Study on proper learning under relaxed worst-case robust loss for VC classes.
problem Proper adversarially robust PAC learning under relaxed worst-case robust loss.
method Introduced a family of robust loss relaxations and showed their effectiveness for proper learnability.
result VC classes are properly PAC learnable with sample complexity close to standard PAC learning setup.
This work proves DP learnability implies online learnability for general classification tasks.
problem Link between differential privacy and online learning for general classification tasks.
method Establishes Ramsey-type theorems for trees to prove DP learnability implies online learnability.
result DP learnability implies online learnability for general classification tasks.
We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missi…
Proper learning is possible with labeled data, but unlabeled data can improve performance.
problem Problems that can only be learned improperly, like multiclass classification.
method Distributional regularization and worst-case performance evaluation.
result Proper learnability is possible under certain conditions involving unlabeled data.
Extends PAC learning theory to handle partial concepts with special properties.
problem Traditional PAC learning theory cannot handle tasks with special data properties.
method Introduces partial concepts and new PAC learning framework.
result Partial concept classes cannot be captured by traditional PAC theory.
No single parameter characterizes the learnability of probability distributions.
problem Finding a parameter to characterize the learnability of probability distributions.
method Analyzing various notions of learnability and showing impossibility results.
result No such parameter exists for characterizing learnability of probability distributions.
Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable provides a way to solve the Applied learning problem. However, the theory requires t…
New findings show modern neural networks have finite sample complexity in o-minimal structures.
problem Understanding the learnability of modern neural networks in a broad context.
method Analyzing feedforward neural networks definable in o-minimal structures.
result Modern neural networks, including MLPs, CNNs, GNNs, and transformers, have finite sample complexity in the agnostic PAC setting.
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoret…
Private classification and online prediction are shown to be equivalent.
problem Learning with differential privacy and online prediction equivalence.
method Introducing global stability and proving equivalence between online learnability and private PAC learnability.
result Every concept class with finite Littlestone dimension can be learned by a differentially-private algorithm.
Study shows multi-source learning is more resilient to adversarial corruption than single-source learning.
problem Learning from multiple untrusted data sources, especially when some are adversarially corrupted.
method Analyzed the scenario where an adversary can corrupt a fixed fraction of data sources, derived a generalization bound for this setting.
result PAC-learnability is possible in the multi-source setting even when some data sources are adversarially corrupted.
Unified model for interactive estimation with improved learnability measure.
problem Improving learnability in interactive estimation models.
method Introducing a combinatorial measure (dissimilarity dimension) and a general algorithm with polynomial bounds.
result Unified model subsumes statistical-query learning and structured bandits.
This research sets limits on how complex multi-class learning problems can be.
problem Understanding the complexity of multi-class classification problems.
method Established upper bounds on Natarajan dimensions for specific function classes.
result Upper bounds on Natarajan dimensions for multi-class decision trees, random forests, and neural networks.
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.
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class C under the family of all non-atomic (diffuse) measures on the domain Ω. The uniform Glivenko--Cantelli property with respect to non-atomic measures is no longer a necessary condition, and consisten…
Defines computable learning for binary classification over metric spaces.
problem Defines computable PAC learning for binary classification over computable metric spaces.
method Provides sufficient conditions for ERM learners to be computable and bounds the strong Weihrauch degree of an ERM learner.
result Gives a hypothesis class that does not admit any proper computable PAC learner with computable sample function.
Study extends learnability equivalence to multi-class and regression, overcoming binary classification limits.
problem Equivalence of online and private learnability in multi-class and regression settings.
method Introduced a novel Littlestone dimension variant and threshold functions for multi-class classification.
result Online learnability implies private learnability in multi-class classification but not in regression.
We study the sample complexity of private synthetic data generation over an unbounded sized class of statistical queries, and show that any class that is privately proper PAC learnable admits a private synthetic data generator (perhaps non-efficient). Previous work on synthetic data generators focused on the case that …
Study shows how many domains are needed for generalization, using a new measure called domain shattering dimension.
problem How many domains are needed for domain generalization?
method Introduced a new combinatorial measure called the domain shattering dimension to model domain sample complexity.
result Established a tight quantitative relationship between domain shattering dimension and classic VC dimension.
Develops a theory to make learning solutions fair and safe.
problem Ensuring learning solutions are unbiased and safe in critical applications.
method Generates a generalization theory based on PAC learning framework, introduces constrained learning algorithm.
result Proves that constrained learning is as learnable as unconstrained learning, provides practical algorithm.
We consider the Domain Adaptation problem, also known as the covariate shift problem, where the distributions that generate the training and test data differ while retaining the same labeling function. This problem occurs across a large range of practical applications, and is related to the more general challenge of tr…
Study risk-sensitive reinforcement learning with optimized certainty equivalents.
problem Risk-sensitive reinforcement learning in finite discounted MDPs.
method Analyzed a simple model-based approach and derived PAC sample complexity bounds.
result Established tight sample complexity bounds for value and policy learning.
Paper generalizes strategic classification framework and introduces SVC for PAC-learning.
problem Strategic manipulation of testing data to fool classifiers.
method Unified framework for strategic classification, strategic VC-dimension (SVC).
result Characterizes the learnability and computational tractability of linear classifiers.
Paper investigates learnability of OOD detection under various conditions.
problem Learnability of OOD detection under different scenarios.
method Investigates PAC learning theory, proves impossibility theorems, and provides necessary and sufficient conditions.
result Some conditions for learnability of OOD detection may not hold in practical scenarios.
Proposes a new approach to regression learning that addresses overfitting and underfitting.
problem Regression learning issues, including overfitting and underfitting.
method Introduces epsilon-Confidence Approximately Correct (epsilon CoAC) framework using Kullback Leibler divergence.
result Demonstrates improved learnability and accuracy compared to cross-validation.
Compact learning results across various loss functions.
problem Understanding sample complexity in transductive learning.
method Analyzing finite projections and sample complexities for different loss functions.
result Exact compactness of sample complexity holds broadly across realizable and agnostic learning.
Paper investigates OOD detection learnability under various conditions.
problem Learnability of OOD detection under diverse and unknown test data.
method PAC learning theory applied to OOD detection, proving impossibility theorems and necessary conditions.
result Some conditions for learnability hold in practical scenarios.
In this paper, we analyze PAC learnability from labels produced by crowdsourcing. In our setting, unlabeled examples are drawn from a distribution and labels are crowdsourced from workers who operate under classification noise, each with their own noise parameter. We develop an end-to-end crowdsourced PAC learning algo…
New findings show learnable distributions remain learnable even with noisy or adversarial perturbations.
problem Learning from perturbed samples in high-dimensional spaces.
method Developed a perturbation-quantization framework to analyze additive noise and adversarial corruption models.
result Sample compressible families remain learnable even under noisy or adversarial perturbations.
We clarify measurability assumptions in the agnostic PAC learning theorem.
problem Measurability assumptions in the Fundamental Theorem of Statistical Learning.
method Measure-theoretic scrutiny of existing proofs to extract minimal assumptions.
result Sound statement and detailed proof of the Fundamental Theorem in the agnostic setting.
New complexity measure helps in agnostic reinforcement learning with or without access to MDP dynamics.
problem Understanding the number of rounds needed to learn an ε-suboptimal policy in unknown MDPs.
method Introducing spanning capacity as a new complexity measure and developing POPLER algorithm.
result There is a separation between generative and online access models for agnostic learnability.
New findings on PAC learning and marginal distribution estimation.
problem Understanding how PAC learning relates to marginal distribution estimation under distributional constraints.
method Revisited the connection between PAC learning, uniform convergence, and density estimation, considering a known family of marginal distributions.
result PAC learning is sandwiched between two refined models of density estimation, differing only in whether the learner knows the set of well-estimated events in H.
This paper explores how boolean formulas can be learned by deep neural networks.
problem Understanding the learnability of boolean formulas by deep neural networks.
method Analysis of boolean formulas associated with model-sampling benchmarks, combinatorial optimization problems, and random 3-CNFs.
result Neural networks outperform rule-based systems and pure symbolic approaches in learning boolean formulas.
Study on computational aspects of replicable learning, bridging statistical and algorithmic perspectives.
problem Understanding the computational connections between replicability and various learning paradigms.
method Design of replicable learners, lifting framework, and transformation techniques.
result Efficient replicable learners for specific learning problems under various distributions.
Study on the limits of bandit learning, showing hardness and limitations.
problem Understanding the learnability of bandit learning under arbitrary reward functions.
method Investigation into which classes of reward functions are learnable and how they can be learned.
result No combinatorial dimension can characterize bandit learnability, and computational hardness is inherent.