Related papers: On the Computability of Multiclass PAC Learning
We study multiclass PAC learning with bandit feedback, where inputs are classified into one of $K$ possible labels and feedback is limited to whether or not the predicted labels are correct. Our main contribution is in designing a novel…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…
The dichotomy between the challenging nature of obtaining annotations for activities, and the more straightforward nature of data collection from wearables, has resulted in significant interest in the development of techniques that utilize…
We study the problem of learning from multiple untrusted data sources, a scenario of increasing practical relevance given the recent emergence of crowdsourcing and collaborative learning paradigms. Specifically, we analyze the situation in…
Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs…
There has been a recent interest in understanding and characterizing the sample complexity of list learning tasks, where the learning algorithm is allowed to make a short list of $k$ predictions, and we simply require one of the predictions…
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…
The classical PAC sample complexity bounds are stated for any Empirical Risk Minimizer (ERM) and contain an extra logarithmic factor $\log(1/{\epsilon})$ which is known to be necessary for ERM in general. It has been recently shown by…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
Beyond binary classification, learnability can become a logically fragile notion: in EMX, even the class of all finite subsets of $[0,1]$ is learnable in some models of ZFC and not in others. We argue the paradox is operational. The…
We study the problem of adversarially robust learning in the transductive setting. For classes $\mathcal{H}$ of bounded VC dimension, we propose a simple transductive learner that when presented with a set of labeled training examples and a…
This paper presents a parallel adaptive clustering (PAC) algorithm to automatically classify data while simultaneously choosing a suitable number of classes. Clustering is an important tool for data analysis and understanding in a broad set…
How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…
The pioneering method for unsupervised meta-learning, CACTUs, is a clustering-based approach with pseudo-labeling. This approach is model-agnostic and can be combined with supervised algorithms to learn from unlabeled data. However, it…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction…
We use and adapt the Borsuk-Ulam Theorem from topology to derive limitations on list-replicable and globally stable learning algorithms. We further demonstrate the applicability of our methods in combinatorics and topology. We show that,…
A common way to evaluate the reliability of dimensionality reduction (DR) embeddings is to quantify how well labeled classes form compact, mutually separated clusters in the embeddings. This approach is based on the assumption that the…
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…