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.
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.
Example shows learnable distributions not privately learnable.
problem Learnable distributions under non-private conditions not transferable to differential privacy.
method Example of a distribution class learnable up to constant error in total variation distance but not under differential privacy.
result Contradicts conjecture of Ashtiani on learnability under differential privacy.
Characterizes learnability of multioutput functions in various settings.
problem Learning multioutput function classes in batch and online settings.
method Characterizes learnability based on single-output restrictions.
result Complete characterization of learnability in multioutput classification and regression.
Research characterizes learnability of multilabel ranking problems.
problem Learnability of multilabel ranking problems with relevance-score feedback.
method Characterizes learnability in batch and online settings for a large family of ranking losses.
result Characterizes two equivalence classes of ranking losses based on learnability.
We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term of suitable notions of complexity, as well as more recent results that establish …
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.
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.
New learnability criteria for non-iid processes equivalent to online learning.
problem Statistical learning under non-iid stochastic processes is underdeveloped.
method Defined two learnability notions and showed their equivalence to online learning.
result Learnability criteria for non-iid processes are equivalent to online learning.
New approach to nonuniform learnability using measure theory.
problem Nonuniform learnability of hypotheses with varying sample sizes.
method Measure theoretic approach to redefine nonuniform learnability, introducing a new algorithm (Generalize Measure Learnability).
result Achieved statistical consistency in learning countable hypothesis classes.
In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially with its depth. On the practical front, we find that the learnability drops sharply…
New algorithm learns regression models privately under growth condition.
problem Private learning of nonparametric regression models.
method Novel filtering procedure to output stable hypotheses for nonparametric function classes.
result Established first nonparametric private learnability guarantee for diverging fat shattering dimensions.
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue that this type of learnability fits in with other notions such as PAC learnabili…
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.
Characterizes learnability of forgiving 0-1 loss functions in multiclass settings.
problem Understanding when multiclass learning with forgiving 0-1 loss functions is possible.
method Introduces a new combinatorial dimension based on Natarajan Dimension to determine learnability.
result A hypothesis class is learnable if and only if the Generalized Natarajan Dimension is finite.
New findings on depth vs. width in neural networks, showing depth can improve learnability.
problem Understanding the role of depth in neural networks, especially when width is unbounded.
method Analyzing sample complexity for learnability in norm-controlled depth-2 and depth-3 ReLU networks.
result Depth can improve learnability of functions that are otherwise unlearnable with depth-2 networks.
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.
Estimating the relative importance of each sample in a training set has important practical and theoretical value, such as in importance sampling or curriculum learning. This kind of focus on individual samples invokes the concept of sample-wise learnability: How easy is it to correctly learn each sample (cf. PAC learn…
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.
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.
Study reveals how spectral bias affects learnability on real-world data.
problem Understanding how well complex datasets can be learned using kernel methods.
method Use eigenvalues and eigenfunctions from idealized data to reveal spectral bias on real-world data.
result Bound learnability on real-world data using symmetries of realistic kernels.
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…
Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to be more powerful to characterize learnability in the general learning setting und…
Characterizes concept classes for optimistic online learning.
problem Understanding minimal assumptions for online learnability.
method Investigates two questions about concept classes' learnability.
result Characterizes all concept classes for optimistically universal online learnability.
Online learning of linear operators between infinite-dimensional spaces is possible but with limitations.
problem Learning linear operators between infinite-dimensional Hilbert spaces in an online setting.
method Online learning approach for linear operators with bounded p-Schatten norm, proving impossibility for operator norm. result Separation between online learnability and uniform convergence for bounded linear operators.
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.
Two-parameter models can learn high-dimensional targets via gradient flow.
problem Learning high-dimensional targets with limited parameters.
method Gradient flow approach for W<d models. result Two-parameter models can learn targets with arbitrarily high success probability.
While machine learning has proven to be a powerful data-driven solution to many real-life problems, its use in sensitive domains has been limited due to privacy concerns. A popular approach known as **differential privacy** offers provable privacy guarantees, but it is often observed in practice that it could substanti…
We characterize learnability for stochastic noisy bandits, identifying optimal query complexities.
problem Learnability of stochastic noisy bandit models.
method Complete characterization through model class analysis and proof of optimal query complexities.
result Characterization of learnability for stochastic noisy bandit models.
Study online multiclass classification under bandit feedback, extending previous results.
problem Online multiclass classification with bandit feedback, focusing on label space unboundedness.
method Extend Daniely and Helbertal's results, show necessity and sufficiency of Bandit Littlestone dimension for learnability.
result Sequential uniform convergence is necessary but not sufficient for bandit online learnability.
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 learns linear utility functions from comparisons, showing learnability gaps between passive and active learning.
problem Learn linear utility functions from pairwise comparison queries.
method Analyzes passive and active learning settings, considering noise-free and noisy query responses.
result Efficient learnability of linear utilities in passive learning, but not for utility parameters without strong assumptions.
The Information Bottleneck (IB) method (\cite{tishby2000information}) provides an insightful and principled approach for balancing compression and prediction for representation learning. The IB objective I(X;Z)−βI(Y;Z) employs a Lagrange multiplier β to tune this trade-off. However, in practice, not only is β cho…
New insights into learning from distributional adversaries and private data.
problem Understanding minimal assumptions for learning and generalization under distributional constraints.
method Generalized smoothness as a characterization of learnability and privacy under distributional adversaries.
result Near complete characterization of families that admit learnability and privacy under distributional adversaries.
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.
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.
Improved multi-class AdaBoost algorithm with stronger weak learnability condition.
problem Multi-class classification problem with at least two labels.
method Recursive ensemble algorithm inspired by SAMME, strengthening weak learnability condition.
result Final hypothesis converges to correct label with probability 1 and generalization error bounds exponentially.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.
Study analyzes learnability of RKHS under L∞ norm for kernel methods.
problem Understand performance of kernel methods and random feature models.
method Relate L∞ learnability to kernel spectrum decay and establish sample complexity bounds.
result Conditions for efficient L∞ learning of RKHS identified.
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…
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.
Study on when RLVR can learn compositional problems.
problem Understanding when RLVR can learn compositional problems.
method Theoretical analysis of task-advantage ratio to characterize learnability.
result Identified conditions for learnability of compositional problems.
Deep networks can learn functions approximated by shallow networks, but not all functions.
problem The learnability of functions by deep neural networks and the approximation capacity of simpler classes.
method Study the connection between learnability and approximation capacity of functions by deep neural networks and simpler classes.
result A necessary condition for a function to be learnable by deep neural networks is to be approximable by shallow networks.
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.
Study shows limitations and possibilities of learning quantum circuit output distributions.
problem Learnability of output distributions of local quantum circuits.
method Investigated within two oracle models: statistical query model and direct sample access model.
result Output distributions of super-logarithmic depth Clifford circuits are not efficiently learnable in the statistical query model.
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.
Learnable multiclass hypothesis classes don't always have a sample compression scheme of fixed size.
problem The limitation of sample compression schemes for multiclass hypothesis classes.
method Analysis of DS dimension and sample compression schemes.
result Learnable multiclass hypothesis classes do not always have a sample compression scheme of fixed size.