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Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.

When presented with a binary classification problem where the data exhibits severe class imbalance, most standard predictive methods may fail to accurately model the minority class. We present a model based on Generative Adversarial Networks which uses additional regularization losses to map majority samples to corresponding synthetic minority samples. This translation mechanism encourages the synthesized samples to be close to the class boundary. Furthermore, we explore a selection criterion to retain the most useful of the synthesized samples. Experimental results using several downstream classifiers on a variety of tabular class-imbalanced datasets show that the proposed method improves average precision when compared to alternative re-weighting and oversampling techniques.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules or applying parameters to small molecules or biopolymers, making it difficult to optimize both types and parameters to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph neural networks to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using invariance-preserving layers. Since all stages are built from smooth neural functions, the entire process is modular and end-to-end differentiable with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach is not only sufficiently expressive to reproduce legacy atom types, but that it can learn to accurately reproduce and extend existing molecular mechanics force fields. Trained with arbitrary loss functions, it can construct entirely new force fields self-consistently applicable to both biopolymers and small molecules directly from quantum chemical calculations, with superior fidelity than traditional atom or parameter typing schemes. When trained on the same quantum chemical small molecule dataset used to parameterize the openff-1.2.0 small molecule force field augmented with a peptide dataset, the resulting espaloma model shows superior accuracy vis-\`a-vis experiments in computing relative alchemical free energy calculations for a popular benchmark set.

We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.

Bearing fault identification and analysis is an important research area in the field of machinery fault diagnosis. Aiming at the common faults of rolling bearings, we propose a data-driven diagnostic algorithm based on the characteristics of bearing vibrations called multi-size kernel based adaptive convolutional neural network (MSKACNN). Using raw bearing vibration signals as the inputs, MSKACNN provides vibration feature learning and signal classification capabilities to identify and analyze bearing faults. Ball mixing is a ball bearing production quality problem that is difficult to identify using traditional frequency domain analysis methods since it requires high frequency resolutions of the measurement signals and results in a long analyzing time. The proposed MSKACNN is shown to improve the efficiency and accuracy of ball mixing diagnosis. To further demonstrate the effectiveness of MSKACNN in bearing fault identification, a bearing vibration data acquisition system was developed, and vibration signal acquisition was performed on rolling bearings under five different fault conditions including ball mixing. The resulting datasets were used to analyze the performance of our proposed model. To validate the adaptive ability of MSKACNN, fault test data from the Case Western Reserve University Bearing Data Center were also used. Test results show that MSKACNN can identify the different bearing conditions with high accuracy with high generalization ability. We presented an implementation of the MSKACNN as a lightweight module for a real-time bearing fault diagnosis system that is suitable for production.

Policy gradient (PG) estimation becomes a challenge when we are not allowed to sample with the target policy but only have access to a dataset generated by some unknown behavior policy. Conventional methods for off-policy PG estimation often suffer from either significant bias or exponentially large variance. In this paper, we propose the double Fitted PG estimation (FPG) algorithm. FPG can work with an arbitrary policy parameterization, assuming access to a Bellman-complete value function class. In the case of linear value function approximation, we provide a tight finite-sample upper bound on policy gradient estimation error, that is governed by the amount of distribution mismatch measured in feature space. We also establish the asymptotic normality of FPG estimation error with a precise covariance characterization, which is further shown to be statistically optimal with a matching Cramer-Rao lower bound. Empirically, we evaluate the performance of FPG on both policy gradient estimation and policy optimization, using either softmax tabular or ReLU policy networks. Under various metrics, our results show that FPG significantly outperforms existing off-policy PG estimation methods based on importance sampling and variance reduction techniques.

This paper reports on a follow-up study of the work reported in Sakai, which explored suitable evaluation measures for ordinal quantification tasks. More specifically, the present study defines and evaluates, in addition to the quantification measures considered earlier, a few variants of an ordinal quantification measure called Root Normalised Order-aware Divergence (RNOD), as well as a measure which we call Divergence based on Kendall's $\tau$ (DNKT). The RNOD variants represent alternative design choices based on the idea of Sakai's Distance-Weighted sum of squares (DW), while DNKT is designed to ensure that the system's estimated distribution over classes is faithful to the target priorities over classes. As this Priority Preserving Property (PPP) of DNKT may be useful in some applications, we also consider combining some of the existing quantification measures with DNKT. Our experiments with eight ordinal quantification data sets suggest that the variants of RNOD do not offer any benefit over the original RNOD at least in terms of system ranking consistency, i.e., robustness of the system ranking to the choice of test data. Of all ordinal quantification measures considered in this study (including Normalised Match Distance, a.k.a. Earth Mover's Distance), RNOD is the most robust measure overall. Hence the design choice of RNOD is a good one from this viewpoint. Also, DNKT is the worst performer in terms of system ranking consistency. Hence, if DNKT seems appropriate for a task, sample size design should take its statistical instability into account.

Extreme multi-label text classification (XMC) aims to tag each input text with the most relevant labels from an extremely large label set, such as those that arise in product categorization and e-commerce recommendation. Recently, pretrained language representation models such as BERT achieve remarkable state-of-the-art performance across a wide range of NLP tasks including sentence classification among small label sets (typically fewer than thousands). Indeed, there are several challenges in applying BERT to the XMC problem. The main challenges are: (i) the difficulty of capturing dependencies and correlations among labels, whose features may come from heterogeneous sources, and (ii) the tractability to scale to the extreme label setting as the model size can be very large and scale linearly with the size of the output space. To overcome these challenges, we propose X-BERT, the first feasible attempt to finetune BERT models for a scalable solution to the XMC problem. Specifically, X-BERT leverages both the label and document text to build label representations, which induces semantic label clusters in order to better model label dependencies. At the heart of X-BERT is finetuning BERT models to capture the contextual relations between input text and the induced label clusters. Finally, an ensemble of the different BERT models trained on heterogeneous label clusters leads to our best final model. Empirically, on a Wiki dataset with around 0.5 million labels, X-BERT achieves new state-of-the-art results where the precision@1 reaches 67:80%, a substantial improvement over 32.58%/60.91% of deep learning baseline fastText and competing XMC approach Parabel, respectively. This amounts to a 11.31% relative improvement over Parabel, which is indeed significant since the recent approach SLICE only has 5.53% relative improvement.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.