We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space X and the goal is to order all possible observations x in X by means of a scoring function s: X R so that s(X) and Y tend to increase or decrease together with highest probability. This problem generalizes bi/multi-partite ranking to a certain extent and the task of finding optimal scoring functions s(x) can be naturally cast as optimization of a dedicated functional criterion, called the IROC curve here, or as maximization of the Kendall τ related to the pair (s(X), Y). From the theoretical side, we describe the optimal elements of this problem and provide statistical guarantees for empirical Kendall τ maximization under appropriate conditions for the class of scoring function candidates. We also propose a recursive statistical learning algorithm tailored to empirical IROC curve optimization and producing a piecewise constant scoring function that is fully described by an oriented binary tree. Preliminary numerical experiments highlight the difference in nature between regression and continuous ranking and provide strong empirical evidence of the performance of empirical optimizers of the criteria proposed.

Decomposing convolutional filters over a set of filter atoms allows efficiently modeling and sampling from a subspace of high-dimensional filters.

Tabular data are fundamental in common machine learning applications, ranging from finance to genomics and healthcare. This paper focuses on tabular regression tasks, a field where deep learning (DL) methods are not consistently superior to machine learning (ML) models due to the challenges posed by irregular target functions inherent in tabular data, causing sensitive label changes with minor variations from features. To address these issues, we propose a novel Arithmetic-Aware Pre-training and Adaptive-Regularized Fine-tuning framework (APAR), which enables the model to fit irregular target function in tabular data while reducing the negative impact of overfitting. In the pre-training phase, APAR introduces an arithmetic-aware pretext objective to capture intricate sample-wise relationships from the perspective of continuous labels. In the fine-tuning phase, a consistency-based adaptive regularization technique is proposed to self-learn appropriate data augmentation. Extensive experiments across 10 datasets demonstrated that APAR outperforms existing GBDT-, supervised NN-, and pretrain-finetune NN-based methods in RMSE (+9.43% $\sim$ 20.37%), and empirically validated the effects of pre-training tasks, including the study of arithmetic operations. Our code and data are publicly available at https://github.com/johnnyhwu/APAR.

The ms tries to solve a problem called continuous ranking, which is an extension of bipartite ranking. The idea of continuous ranking is to find a score function that increase or decrease with output y with highest probability. In bipartite ranking, each data point x is given a binary label y \in { 1, -1}. The goal is to find a score function s(x) such that the difference of p(s(x) t y 1) and p(s(x) t y -1) is maximal for all threshold t. This can be achieved by maximizing AUC of the score function. The ms extends the bipartite ranking idea for continuous output Y, by introducing a threshold y to separate the data into two ordered parts.

It is a well-known challenge to learn an unbiased ranker with biased feedback. Unbiased learning-to-rank(LTR) algorithms, which are verified to model the relative relevance accurately based on noisy feedback, are appealing candidates and have already been applied in many applications with single categorical labels, such as user click signals. Nevertheless, the existing unbiased LTR methods cannot properly handle continuous feedback, which are essential for many industrial applications, such as content recommender systems. To provide personalized high-quality recommendation results, recommender systems need model both categorical and continuous biased feedback, such as click and dwell time. Accordingly, we design a novel unbiased LTR algorithm to tackle the challenges, which innovatively models position bias in the pairwise fashion and introduces the pairwise trust bias to separate the position bias, trust bias, and user relevance explicitly and can work for both continuous and categorical feedback. Experiment results on public benchmark datasets and internal live traffic of a large-scale recommender system at Tencent News show superior results for continuous labels and also competitive performance for categorical labels of the proposed method.

Traditionally, in paralinguistic analysis for emotion detection from speech, emotions have been identified with discrete or dimensional (continuous-valued) labels. Accordingly, models that have been proposed for emotion detection use one or the other of these label types. However, psychologists like Russell and Plutchik have proposed theories and models that unite these views, maintaining that these representations have shared and complementary information. This paper is an attempt to validate these viewpoints computationally. To this end, we propose a model to jointly predict continuous and discrete emotional attributes and show how the relationship between these can be utilized to improve the robustness and performance of emotion recognition tasks. Our approach comprises multi-task and hierarchical multi-task learning frameworks that jointly model the relationships between continuous-valued and discrete emotion labels. Experimental results on two widely used datasets (IEMOCAP and MSPPodcast) for speech-based emotion recognition show that our model results in statistically significant improvements in performance over strong baselines with non-unified approaches. We also demonstrate that using one type of label (discrete or continuous-valued) for training improves recognition performance in tasks that use the other type of label. Experimental results and reasoning for this approach (called the mismatched training approach) are also presented.

Nowadays, recommender systems already impact almost every facet of peoples lives. To provide personalized high quality recommendation results, conventional systems usually train pointwise rankers to predict the absolute value of objectives and leverage a distinct shallow tower to estimate and alleviate the impact of position bias. However, with such a training paradigm, the optimization target differs a lot from the ranking metrics valuing the relative order of top ranked items rather than the prediction precision of each item. Moreover, as the existing system tends to recommend more relevant items at higher positions, it is difficult for the shallow tower based methods to precisely attribute the user feedback to the impact of position or relevance. Therefore, there exists an exciting opportunity for us to get enhanced performance if we manage to solve the aforementioned issues. Unbiased learning to rank algorithms, which are verified to model the relative relevance accurately based on noisy feedback, are appealing candidates and have already been applied in many applications with single categorical labels, such as user click signals. Nevertheless, the existing unbiased LTR methods cannot properly handle multiple feedback incorporating both categorical and continuous labels. Accordingly, we design a novel unbiased LTR algorithm to tackle the challenges, which innovatively models position bias in the pairwise fashion and introduces the pairwise trust bias to separate the position bias, trust bias, and user relevance explicitly. Experiment results on public benchmark datasets and internal live traffic show the superior results of the proposed method for both categorical and continuous labels.

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space X and the goal is to order all possible observations x in X by means of a scoring function s: X R so that s(X) and Y tend to increase or decrease together with highest probability. This problem generalizes bi/multi-partite ranking to a certain extent and the task of finding optimal scoring functions s(x) can be naturally cast as optimization of a dedicated functional cri- terion, called the IROC curve here, or as maximization of the Kendall τ related to the pair (s(X), Y). From the theoretical side, we describe the optimal elements of this problem and provide statistical guarantees for empirical Kendall τ maximiza- tion under appropriate conditions for the class of scoring function candidates. We also propose a recursive statistical learning algorithm tailored to empirical IROC curve optimization and producing a piecewise constant scoring function that is fully described by an oriented binary tree.

Excellent ranking power along with well calibrated probability estimates are needed in many classification tasks. In this paper, we introduce a technique, Calibrated Boosting-Forest that captures both. This novel technique is an ensemble of gradient boosting machines that can support both continuous and binary labels. While offering superior ranking power over any individual regression or classification model, Calibrated Boosting-Forest is able to preserve well calibrated posterior probabilities. Along with these benefits, we provide an alternative to the tedious step of tuning gradient boosting machines. We demonstrate that tuning Calibrated Boosting-Forest can be reduced to a simple hyper-parameter selection. We further establish that increasing this hyper-parameter improves the ranking performance under a diminishing return. We examine the effectiveness of Calibrated Boosting-Forest on ligand-based virtual screening where both continuous and binary labels are available and compare the performance of Calibrated Boosting-Forest with logistic regression, gradient boosting machine and deep learning. Calibrated Boosting-Forest achieved an approximately 48% improvement compared to a state-of-art deep learning model. Moreover, it achieved around 95% improvement on probability quality measurement compared to the best individual gradient boosting machine. Calibrated Boosting-Forest offers a benchmark demonstration that in the field of ligand-based virtual screening, deep learning is not the universally dominant machine learning model and good calibrated probabilities can better facilitate virtual screening process.

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their adaptation to non-discrete or continuous node attributes has been limited, mainly for computational issues. Recently, a few kernels especially tailored for this domain, and that trade predictive performance for computational efficiency, have been proposed. In this paper, we propose a graph kernel for complex and continuous nodes' attributes, whose features are tree structures extracted from specific graph visits. The kernel manages to keep the same complexity of state-of-the-art kernels while implicitly using a larger feature space. We further present an approximated variant of the kernel which reduces its complexity significantly. Experimental results obtained on six real-world datasets show that the kernel is the best performing one on most of them. Moreover, in most cases the approximated version reaches comparable performances to current state-of-the-art kernels in terms of classification accuracy while greatly shortening the running times.