Related papers: Online Learning of k-CNF Boolean Functions

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

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.

We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log…

This paper describes a family of probabilistic architectures designed for online learning under the logarithmic loss. Rather than relying on non-linear transfer functions, our method gains representational power by the use of data…

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…

It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and…

Most PAC-Bayesian bounds hold in the batch learning setting where data is collected at once, prior to inference or prediction. This somewhat departs from many contemporary learning problems where data streams are collected and the…

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…

In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We…

We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded…

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…

Recent advances have clarified theoretical learning accuracy in Bayesian inference, revealing that the asymptotic behavior of metrics such as generalization loss and free energy, assessing predictive accuracy, is dictated by a rational…

Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…

We prove that any submodular function f: {0,1}^n -> {0,1,...,k} can be represented as a pseudo-Boolean 2k-DNF formula. Pseudo-Boolean DNFs are a natural generalization of DNF representation for functions with integer range. Each term in…

Noise-tolerant PAC learning of linear models has been of central interests in machine learning community since the last century. In recent years, many computationally-efficient algorithms have been proposed for the problem of learning…

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…