Surrogate regret bounds for generalized classification performance metrics

We consider optimization of generalized performance metrics for binary classification by means of surrogate losses. We focus on a class of metrics, which are linear-fractional functions of the false positive and false negative rates (examples of which include $F_{\beta}$-measure, Jaccard similarity coefficient, AM measure, and many others). Our analysis concerns the following two-step procedure. First, a real-valued function $f$ is learned by minimizing a surrogate loss for binary classification on the training sample. It is assumed that the surrogate loss is a strongly proper composite loss function (examples of which include logistic loss, squared-error loss, exponential loss, etc.). Then, given $f$, a threshold $\widehat{\theta}$ is tuned on a separate validation sample, by direct optimization of the target performance metric. We show that the regret of the resulting classifier (obtained from thresholding $f$ on $\widehat{\theta}$) measured with respect to the target metric is upperbounded by the regret of $f$ measured with respect to the surrogate loss. We also extend our results to cover multilabel classification and provide regret bounds for micro- and macro-averaging measures. Our findings are further analyzed in a computational study on both synthetic and real data sets.Comment: 22 page

An analysis of chaining in multi-label classification

The idea of classifier chains has recently been introduced as a promising technique for multi-label classification. However, despite being intuitively appealing and showing strong performance in empirical studies, still very little is known about the main principles underlying this type of method. In this paper, we provide a detailed probabilistic analysis of classifier chains from a risk minimization perspective, thereby helping to gain a better understanding of this approach. As a main result, we clarify that the original chaining method seeks to approximate the joint mode of the conditional distribution of label vectors in a greedy manner. As a result of a theoretical regret analysis, we conclude that this approach can perform quite poorly in terms of subset 0/1 loss. Therefore, we present an enhanced inference procedure for which the worst-case regret can be upper-bounded far more tightly. In addition, we show that a probabilistic variant of chaining, which can be utilized for any loss function, becomes tractable by using Monte Carlo sampling. Finally, we present experimental results confirming the validity of our theoretical findings

INTERPRETATION OF EXPERIMENTS IN PAUL TRAP

Chosen aspects of laser spectroscopy in a Paul trap have been discussed. On the example of interpretation of the experimental results for europium ion the advantages of the use of semiempirical atomicstructure calculations have been proved. For the calculations a computer package, prepared and adopted by ourselves to be used on vector computers, has been applied.Pozna

COMPUTATIONAL PACKAGE FOR ANALYSIS OF THE FINE STRUCTURE OF A FREE ATOM

This work describes some computer programs that are available in compiled form for users of the SGI Power Challenge machine at Poznań Supercomputing and Networking Center. These programs give apossibility to solve very complex problems in the structure of free atoms using experimental data. The procedure of determination of the Slater integrals, spin-orbit parameters and also the parameters representingthe effect of virtual excitations (many-body effects) is described. The program gives the propositions of the spectroscopic designations of energy levels. Moreover, the wavefunctions in intermediate coupling scheme in many-configurations approximation for the selected configuration system can be obtained.Pozna

Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach

AbstractThe rough sets theory has proved to be a useful mathematical tool for the analysis of a vague description of objects. One of extensions of the classic theory is the Dominance-based Set Approach (DRSA) that allows analysing preference-ordered data. The analysis ends with a set of decision rules induced from rough approximations of decision classes. The role of the decision rules is to explain the analysed phenomena, but they may also be applied in classifying new, unseen objects. There are several strategies of decision rule induction. One of them consists in generating the exhaustive set of minimal rules. In this paper we present an algorithm based on Boolean reasoning techniques that follows this strategy with in DRSA

Generalized test utilities for long-tail performance in extreme multi-label classification

Extreme multi-label classification (XMLC) is the task of selecting a small subset of relevant labels from a very large set of possible labels. As such, it is characterized by long-tail labels, i.e., most labels have very few positive instances. With standard performance measures such as precision@k, a classifier can ignore tail labels and still report good performance. However, it is often argued that correct predictions in the tail are more "interesting" or "rewarding," but the community has not yet settled on a metric capturing this intuitive concept. The existing propensity-scored metrics fall short on this goal by confounding the problems of long-tail and missing labels. In this paper, we analyze generalized metrics budgeted "at k" as an alternative solution. To tackle the challenging problem of optimizing these metrics, we formulate it in the expected test utility (ETU) framework, which aims to optimize the expected performance on a fixed test set. We derive optimal prediction rules and construct computationally efficient approximations with provable regret guarantees and robustness against model misspecification. Our algorithm, based on block coordinate ascent, scales effortlessly to XMLC problems and obtains promising results in terms of long-tail performance.Comment: This is the authors' version of the work accepted to NeurIPS 2023; the final version of the paper, errors and typos corrected, and minor modifications to improve clarit