Unconfused Ultraconservative Multiclass Algorithms

We tackle the problem of learning linear classifiers from noisy datasets in a multiclass setting. The two-class version of this problem was studied a few years ago by, e.g. Bylander (1994) and Blum et al. (1996): in these contributions, the proposed approaches to fight the noise revolve around a Perceptron learning scheme fed with peculiar examples computed through a weighted average of points from the noisy training set. We propose to build upon these approaches and we introduce a new algorithm called UMA (for Unconfused Multiclass additive Algorithm) which may be seen as a generalization to the multiclass setting of the previous approaches. In order to characterize the noise we use the confusion matrix as a multiclass extension of the classification noise studied in the aforementioned literature. Theoretically well-founded, UMA furthermore displays very good empirical noise robustness, as evidenced by numerical simulations conducted on both synthetic and real data. Keywords: Multiclass classification, Perceptron, Noisy labels, Confusion MatrixComment: ACML, Australia (2013

Exploring Parity Challenges in Reinforcement Learning through Curriculum Learning with Noisy Labels

This paper delves into applying reinforcement learning (RL) in strategy games, particularly those characterized by parity challenges, as seen in specific positions of Go and Chess and a broader range of impartial games. We propose a simulated learning process, structured within a curriculum learning framework and augmented with noisy labels, to mirror the intricacies of self-play learning scenarios. This approach thoroughly analyses how neural networks (NNs) adapt and evolve from elementary to increasingly complex game positions. Our empirical research indicates that even minimal label noise can significantly impede NNs' ability to discern effective strategies, a difficulty that intensifies with the growing complexity of the game positions. These findings underscore the urgent need for advanced methodologies in RL training, specifically tailored to counter the obstacles imposed by noisy evaluations. The development of such methodologies is crucial not only for enhancing NN proficiency in strategy games with significant parity elements but also for broadening the resilience and efficiency of RL systems across diverse and complex environments

Bayes classifier cannot be learned from noisy responses with unknown noise rates

Training a classifier with noisy labels typically requires the learner to specify the distribution of label noise, which is often unknown in practice. Although there have been some recent attempts to relax that requirement, we show that the Bayes decision rule is unidentified in most classification problems with noisy labels. This suggests it is generally not possible to bypass/relax the requirement. In the special cases in which the Bayes decision rule is identified, we develop a simple algorithm to learn the Bayes decision rule, that does not require knowledge of the noise distribution.Comment: Invited to present in ICLR Tiny Paper 202

The Power of Localization for Efficiently Learning Linear Separators with Noise

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label noise model. For malicious noise, where the adversary can corrupt both the label and the features, we provide a polynomial-time algorithm for learning linear separators in $\Re^d$ under isotropic log-concave distributions that can tolerate a nearly information-theoretically optimal noise rate of $\eta = \Omega(\epsilon)$. For the adversarial label noise model, where the distribution over the feature vectors is unchanged, and the overall probability of a noisy label is constrained to be at most $\eta$, we also give a polynomial-time algorithm for learning linear separators in $\Re^d$ under isotropic log-concave distributions that can handle a noise rate of $\eta = \Omega\left(\epsilon\right)$. We show that, in the active learning model, our algorithms achieve a label complexity whose dependence on the error parameter $\epsilon$ is polylogarithmic. This provides the first polynomial-time active learning algorithm for learning linear separators in the presence of malicious noise or adversarial label noise.Comment: Contains improved label complexity analysis communicated to us by Steve Hannek

A Complete Characterization of Statistical Query Learning with Applications to Evolvability

Statistical query (SQ) learning model of Kearns (1993) is a natural restriction of the PAC learning model in which a learning algorithm is allowed to obtain estimates of statistical properties of the examples but cannot see the examples themselves. We describe a new and simple characterization of the query complexity of learning in the SQ learning model. Unlike the previously known bounds on SQ learning our characterization preserves the accuracy and the efficiency of learning. The preservation of accuracy implies that that our characterization gives the first characterization of SQ learning in the agnostic learning framework. The preservation of efficiency is achieved using a new boosting technique and allows us to derive a new approach to the design of evolutionary algorithms in Valiant's (2006) model of evolvability. We use this approach to demonstrate the existence of a large class of monotone evolutionary learning algorithms based on square loss performance estimation. These results differ significantly from the few known evolutionary algorithms and give evidence that evolvability in Valiant's model is a more versatile phenomenon than there had been previous reason to suspect.Comment: Simplified Lemma 3.8 and it's application

Detecting Label Noise via Leave-One-Out Cross-Validation

We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted sample points using Gaussian process regression. A heteroscedastic noise model is employed, in which additive Gaussian noise terms with independent variances are associated with each and all of the observed labels. Optimizing the noise model using maximum likelihood estimation leads to the containment of the GPR model's predictive error by the posterior standard deviation in leave-one-out cross-validation. A multiplicative update scheme is proposed for solving the maximum likelihood estimation problem under non-negative constraints. While we provide proof of convergence for certain special cases, the multiplicative scheme has empirically demonstrated monotonic convergence behavior in virtually all our numerical experiments. We show that the presented method can pinpoint corrupted sample points and lead to better regression models when trained on synthetic and real-world scientific data sets