Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem given a probabilistic program asks whether the program terminates with probability 1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). While deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to academic examples. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of realworld programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on abstractions of real-world programs to demonstrate the effectiveness of our approach.Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs 1:3Our contributions. In this work our main contributions range from theoretical foundations of lexicographic RSMs, to algorithmic approaches for them, to experimental results showing their applicability to programs. We describe our main contributions below:
Extreme multi-label classification (XML) involves tagging a data point with its most relevant subset of labels from an extremely large label set, with several applications such as product-to-product recommendation with millions of products. Although leading XML algorithms scale to millions of labels, they largely ignore label metadata such as textual descriptions of the labels. On the other hand, classical techniques that can utilize label metadata via representation learning using deep networks struggle in extreme settings. This paper develops the DECAF algorithm that addresses these challenges by learning models enriched by label metadata that jointly learn model parameters and feature representations using deep networks and offer accurate classification at the scale of millions of labels. DECAF makes specific contributions to model architecture design, initialization, and training, enabling it to offer up to 2-6% more accurate prediction than leading extreme classifiers on publicly available benchmark product-to-product recommendation datasets, such as LF-AmazonTitles-1.3M. At the same time, DECAF was found to be up to 22× faster at inference than leading deep extreme classifiers, which makes it suitable for real-time applications that require predictions within a few milliseconds. The code for DECAF is available at the following URL https://github.com/Extreme-classification/DECAF.
Deep extreme classification (XC) seeks to train deep architectures that can tag a data point with its most relevant subset of labels from an extremely large label set. The core utility of XC comes from predicting labels that are rarely seen during training. Such rare labels hold the key to personalized recommendations that can delight and surprise a user. However, the large number of rare labels and small amount of training data per rare label offer significant statistical and computational challenges. State-of-the-art deep XC methods attempt to remedy this by incorporating textual descriptions of labels but do not adequately address the problem. This paper presents ECLARE, a scalable deep learning architecture that incorporates not only label text, but also label correlations, to offer accurate real-time predictions within a few milliseconds. Core contributions of ECLARE include a frugal architecture and scalable techniques to train deep models along with label correlation graphs at the scale of millions of labels. In particular, ECLARE offers predictions that are 2-14% more accurate on both publicly available benchmark datasets as well as proprietary datasets for a related products recommendation task sourced from the Bing search engine. Code for ECLARE is available at https://github.com/Extreme-classification/ECLARE CCS CONCEPTS• Computing methodologies → Machine learning; Supervised learning by classification.
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