Related papers: Rigorous Bounds to Retarded Learning

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…

We improve several worst-case bounds for various online learning scenarios from (Auer and Long, Machine Learning, 1999). In particular, we sharpen an upper bound for delayed ambiguous reinforcement learning by a factor of 2 and an upper…

We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp…

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2,…

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry…

We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected…

Understanding the accuracy limits of machine learning algorithms is essential for data scientists to properly measure performance so they can continually improve their models' predictive capabilities. This study empirically verified the…

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of…

Neutrosophic Over-/Under-/Off-Set and -Logic were defined by the author in 1995 and published for the first time in 2007. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is over 1},…

We study a variant of prediction with expert advice where the learner's action at round $t$ is only allowed to depend on losses on a specific subset of the rounds (where the structure of which rounds' losses are visible at time $t$ is…

The aim of this paper is to give a short overview on error bounds and to provide the first bricks of a unified theory. Inspired by the works of [8, 15, 13, 16, 10], we show indeed the centrality of the Lojasiewicz gradient inequality. For…

In this paper we extend the work of Owen (2007) by deriving a second order expansion for the slope parameter in logistic regression, when the size of the majority class is unbounded and the minority class is finite. More precisely, we…

Learning, especially rapid learning, is critical for survival. However, learning is hard: a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of…

We prove the first generalization bound for large-margin halfspaces that is asymptotically tight in the tradeoff between the margin, the fraction of training points with the given margin, the failure probability and the number of training…

We develop a new approach to obtaining high probability regret bounds for online learning with bandit feedback against an adaptive adversary. While existing approaches all require carefully constructing optimistic and biased loss…

We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm…