Classification with unknown class-conditional label noise on non-compact feature spaces

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditional label noise have required that the regression function is close to its extrema on sets of large measure. We shall consider this problem in the setting of non-compact metric spaces, where the regression function need not attain its extrema. In this setting we determine the minimax optimal learning rates (up to logarithmic factors). The rate displays interesting threshold behaviour: When the regression function approaches its extrema at a sufficient rate, the optimal learning rates are of the same order as those obtained in the label-noise free setting. If the regression function approaches its extrema more gradually then classification performance necessarily degrades. In addition, we present an adaptive algorithm which attains these rates without prior knowledge of either the distributional parameters or the local density. This identifies for the first time a scenario in which finite sample rates are achievable in the label noise setting, but they differ from the optimal rates without label noise

Fast rates for a kNN classifier robust to unknown asymmetric label noise

We consider classification in the presence of class-dependent asymmetric label noise with unknown noise probabilities. In this setting, identifiability conditions are known, but additional assumptions were shown to be required for finite sample rates, and so far only the parametric rate has been obtained. Assuming these identifiability conditions, together with a measure-smoothness condition on the regression function and Tsybakov's margin condition, we show that the Robust kNN classifier of Gao et al. attains, the minimax optimal rates of the noise-free setting, up to a log factor, even when trained on data with unknown asymmetric label noise. Hence, our results provide a solid theoretical backing for this empirically successful algorithm. By contrast the standard kNN is not even consistent in the setting of asymmetric label noise. A key idea in our analysis is a simple kNN based method for estimating the maximum of a function that requires far less assumptions than existing mode estimators do, and which may be of independent interest for noise proportion estimation and randomised optimisation problems.Comment: ICML 201

Optimistic Bounds for Multi-output Prediction

We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression, multi-class classification and multi-label classification. We begin our analysis by introducing the self-bounding Lipschitz condition for multi-output loss functions, which interpolates continuously between a classical Lipschitz condition and a multi-dimensional analogue of a smoothness condition. We then show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which are minimax optimal up to logarithmic factors. The proof exploits local Rademacher complexity combined with a powerful minoration inequality due to Srebro, Sridharan and Tewari. As an application we derive a state-of-the-art generalization bound for multi-class gradient boosting

Menguji Kekuatan Bahan Elektroplating Pelapisan Nikel pada Substrat Besi dengan Uji Impak (Impact Test)

Telah dilakukan penelitian tentang proses elektroplating dengan logam nikel sebagai pelapis dari logam besi. Proses ini dilakukan dengan memvariasi waktu dan temperaturnya. Metode yang digunakan dalam penelitian ini adalah metode pengujian impak terhadap sampel yang telah dielektroplating. Dari hasil penelitian diperoleh bahwa pada masing-masing sampel yang telah di uji impak untuk temperatur yang bervariasi (35_C,40_C,45_C, 50_C, dan 55_C) dengan waktu elektroplating konstan, didapatkan bahwa semakin tinggi temperatur saat elektropating, semakin besar energi impak yang di butuhkan untuk merusak lapisan sampel. Sedangkan pengujian untuk waktu yang bervariasi (8 menit, 10 menit , 13 menit dan 15 menit) pada temperatur konstan menunjukkan bahwa semakin lama waktu sampel yang di elektropating, semakin besar energi impak yang di butuhkan untuk merusak lapisan sampel tersebut