Related papers: Resource-bounded Dimension in Computational Learni…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…
Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension,…
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve…
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 recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted in this paper to accommodate semi-infinite inputs so that it…
We develop a framework using Hilbert spaces as a proxy to analyze PAC learning problems with structural properties. We consider a joint Hilbert space incorporating the relation between the true label and the predictor under a joint…
In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…
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…
Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and…
In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$, introduced by Zilles…
Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
In recent years, researchers have made significant progress in devising reinforcement-learning algorithms for optimizing linear temporal logic (LTL) objectives and LTL-like objectives. Despite these advancements, there are fundamental…
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
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 connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so…
A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary…
Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…