Related papers: On the equivalence of Occam algorithms

Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by [Vitanyi and Chater, 2017] and [Bienvenu et al., 2014] has adapted this framework to the study of…

Many conventional learning algorithms rely on loss functions other than the natural 0-1 loss for computational efficiency and theoretical tractability. Among them are approaches based on absolute loss (L1 regression) and square loss (L2…

$ \newcommand{\eps}{\varepsilon} $In learning theory, the VC dimension of a concept class $C$ is the most common way to measure its "richness." In the PAC model $$ \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big) $$ examples are…

Static program analysis today takes an analytical approach which is quite suitable for a well-scoped system. Data- and control-flow is taken into account. Special cases such as pointers, procedures, and undefined behavior must be handled. A…

We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence. In an influential paper, Valiant recognised that the challenge of learning should be…

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…

We consider a partial-feedback variant of the well-studied online PCA problem where a learner attempts to predict a sequence of $d$-dimensional vectors in terms of a quadratic loss, while only having limited feedback about the environment's…

This paper presents new experimental evidence against the utility of Occam's razor. A~systematic procedure is presented for post-processing decision trees produced by C4.5. This procedure was derived by rejecting Occam's razor and instead…

We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…

For any partial combinatory algebra (PCA for short) A, the class of A-representable partial functions from N to A quotiented by the filter of cofinite sets of N, is a PCA such that the representable partial functions are exactly the…

We revisit the framework of Smart PAC learning, which seeks supervised learners which compete with semi-supervised learners that are provided full knowledge of the marginal distribution on unlabeled data. Prior work has shown that such…

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…

Machine learning is now ubiquitous in societal decision-making, for example in evaluating job candidates or loan applications, and it is increasingly important to take into account how classified agents will react to the learning…

We study the problem of computable multiclass learnability within the Probably Approximately Correct (PAC) learning framework of Valiant (1984). In the recently introduced computable PAC (CPAC) learning framework of Agarwal et al. (2020),…

We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the…

This survey paper gives an overview of various known results on learning classes of Boolean functions in Valiant's Probably Approximately Correct (PAC) learning model and its commonly studied variants.

This paper's first aim is to prove a modernized Occam's razor beyond a reasonable doubt. To summarize the main argument in one sentence: If we consider all possible, intelligible, scientific models of ever-higher complexity, democratically,…

Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…

We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…