In classification problems, models must predict a class label based on the input data features. However, class labels are organized hierarchically in many datasets. While a classification task is often defined at a specific level of this hierarchy, training can utilize a finer granularity of labels. Empirical evidence suggests that such fine-grained training can enhance performance. In this work, we investigate the generality of this observation and explore its underlying causes using both real and synthetic datasets. We show that training on fine-grained labels does not universally improve classification accuracy. Instead, the effectiveness of this strategy depends critically on the geometric structure of the data and its relations with the label hierarchy. Additionally, factors such as dataset size and model capacity significantly influence whether fine-grained labels provide a performance benefit.

Spreadsheets are widely recognized as the most popular end-user programming tools, which blend the power of formula-based computation, with an intuitive table-based interface. Today, spreadsheets are used by billions of users to manipulate tables, most of whom are neither database experts nor professional programmers. Despite the success of spreadsheets, authoring complex formulas remains challenging, as non-technical users need to look up and understand non-trivial formula syntax. To address this pain point, we leverage the observation that there is often an abundance of similar-looking spreadsheets in the same organization, which not only have similar data, but also share similar computation logic encoded as formulas. We develop an Auto-Formula system that can accurately predict formulas that users want to author in a target spreadsheet cell, by learning and adapting formulas that already exist in similar spreadsheets, using contrastive-learning techniques inspired by "similar-face recognition" from compute vision. Extensive evaluations on over 2K test formulas extracted from real enterprise spreadsheets show the effectiveness of Auto-Formula over alternatives. Our benchmark data is available at https://github.com/microsoft/Auto-Formula to facilitate future research.

Decision-tree-based ensemble classification methods (DTEMs) are a prevalent tool for supervised anomaly detection. However, due to the continued growth of datasets, DTEMs result in increasing drawbacks such as growing memory footprints, longer training times, and slower classification latencies at lower throughput. In this paper, we present, design, and evaluate RADE - a DTEM-based anomaly detection framework that augments standard DTEM classifiers and alleviates these drawbacks by relying on two observations: (1) we find that a small (coarse-grained) DTEM model is sufficient to classify the majority of the classification queries correctly, such that a classification is valid only if its corresponding confidence level is greater than or equal to a predetermined classification confidence threshold; (2) we find that in these fewer harder cases where our coarse-grained DTEM model results in insufficient confidence in its classification, we can improve it by forwarding the classification query to one of expert DTEM (fine-grained) models, which is explicitly trained for that particular case. We implement RADE in Python based on scikit-learn and evaluate it over different DTEM methods: RF, XGBoost, AdaBoost, GBDT and LightGBM, and over three publicly available datasets. Our evaluation over both a strong AWS EC2 instance and a Raspberry Pi 3 device indicates that RADE offers competitive and often superior anomaly detection capabilities as compared to standard DTEM methods, while significantly improving memory footprint (by up to 5.46x), training-time (by up to 17.2x), and classification latency (by up to 31.2x).

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of very large systems of algebraic equations. We establish a physically inspired, data-driven coarse-grained model which learns a low- dimensional set of microstructural features that are predictive of the fine-grained model (FG) response. Once learned, those features provide a sharp distribution over the coarse scale effec- tive coefficients of the PDE that are most suitable for prediction of the fine scale model output. This ultimately allows to replace the computationally expensive FG by a generative proba- bilistic model based on evaluating the much cheaper CG several times. Sparsity enforcing pri- ors further increase predictive efficiency and reveal microstructural features that are important in predicting the FG response. Moreover, the model yields probabilistic rather than single-point predictions, which enables the quantification of the unavoidable epistemic uncertainty that is present due to the information loss that occurs during the coarse-graining process.