The Expected Normalized Calibration Error (ENCE) is a popular calibration statistic used in Machine Learning to assess the quality of prediction uncertainties for regression problems. Estimation of the ENCE is based on the binning of calibration data. In this short note, I illustrate an annoying property of the ENCE, i.e. its proportionality to the square root of the number of bins for well calibrated or nearly calibrated datasets. A similar behavior affects the calibration error based on the variance of z-scores (ZVE), and in both cases this property is a consequence of the use of a Mean Absolute Deviation (MAD) statistic to estimate calibration errors. Hence, the question arises of which number of bins to choose for a reliable estimation of calibration error statistics. A solution is proposed to infer ENCE and ZVE values that do not depend on the number of bins for datasets assumed to be calibrated, providing simultaneously a statistical calibration test. It is also shown that the ZVE is less sensitive than the ENCE to outstanding errors or uncertainties.

Web-crawled datasets have enabled remarkable generalization capabilities in recent image-text models such as CLIP (Contrastive Language-Image pre-training) or Flamingo, but little is known about the dataset creation processes. In this work, we introduce a testbed of six publicly available data sources - YFCC, LAION, Conceptual Captions, WIT, RedCaps, Shutterstock - to investigate how pre-training distributions induce robustness in CLIP. We find that the performance of the pre-training data varies substantially across distribution shifts, with no single data source dominating. Moreover, we systematically study the interactions between these data sources and find that combining multiple sources does not necessarily yield better models, but rather dilutes the robustness of the best individual data source. We complement our empirical findings with theoretical insights from a simple setting, where combining the training data also results in diluted robustness. In addition, our theoretical model provides a candidate explanation for the success of the CLIP-based data filtering technique recently employed in the LAION dataset. Overall our results demonstrate that simply gathering a large amount of data from the web is not the most effective way to build a pre-training dataset for robust generalization, necessitating further study into dataset design. Code is available at https://github.com/mlfoundations/clip_quality_not_quantity.

Large pretrained models can be privately fine-tuned to achieve performance approaching that of non-private models. A common theme in these results is the surprising observation that high-dimensional models can achieve favorable privacy-utility trade-offs. This seemingly contradicts known results on the model-size dependence of differentially private convex learning and raises the following research question: When does the performance of differentially private learning not degrade with increasing model size? We identify that the magnitudes of gradients projected onto subspaces is a key factor that determines performance. To precisely characterize this for private convex learning, we introduce a condition on the objective that we term \emph{restricted Lipschitz continuity} and derive improved bounds for the excess empirical and population risks that are dimension-independent under additional conditions. We empirically show that in private fine-tuning of large language models, gradients obtained during fine-tuning are mostly controlled by a few principal components. This behavior is similar to conditions under which we obtain dimension-independent bounds in convex settings. Our theoretical and empirical results together provide a possible explanation for recent successes in large-scale private fine-tuning. Code to reproduce our results can be found at \url{https://github.com/lxuechen/private-transformers/tree/main/examples/classification/spectral_analysis}.

It is often of great interest to quantify how the presence or absence of a particular training data point affects the trained model's performance on test data points. Influence functions is a classical idea for this [Jaeckel, 1972, Hampel, 1974, Cook, 1977] that has recently been adapted to modern deep models and large datasets Koh and Liang [2017]. Influence functions have been applied to explain predictions and produce confidence intervals [Schulam and Saria, 2019], investigate model bias [Brunet et al., 2019, Wang et al., 2019], estimate Shapley values [Jia et al., 2019, Ghorbani and Zou, 2019], improve human trust [Zhou et al., 2019], and craft data poisoning attacks [Koh et al., 2019]. Influence actually has different formalizations. The classic calculus-based estimate (henceforth referred to as continuous influence) involves conceptualizing training loss as a weighted sum over training datapoints, where the weighting of a particular datapoint z can be varied infinitesimally.

Contrastively trained language-image models such as CLIP, ALIGN, and BASIC have demonstrated unprecedented robustness to multiple challenging natural distribution shifts. Since these language-image models differ from previous training approaches in several ways, an important question is what causes the large robustness gains. We answer this question via a systematic experimental investigation. Concretely, we study five different possible causes for the robustness gains: (i) the training set size, (ii) the training distribution, (iii) language supervision at training time, (iv) language supervision at test time, and (v) the contrastive loss function. Our experiments show that the more diverse training distribution is the main cause for the robustness gains, with the other factors contributing little to no robustness. Beyond our experimental results, we also introduce ImageNet-Captions, a version of ImageNet with original text annotations from Flickr, to enable further controlled experiments of language-image training.

For machine learning systems to be reliable, we must understand their performance in unseen, out-of-distribution environments. In this paper, we empirically show that out-of-distribution performance is strongly correlated with in-distribution performance for a wide range of models and distribution shifts. Specifically, we demonstrate strong correlations between in-distribution and out-of-distribution performance on variants of CIFAR-10 & ImageNet, a synthetic pose estimation task derived from YCB objects, satellite imagery classification in FMoW-WILDS, and wildlife classification in iWildCam-WILDS. The strong correlations hold across model architectures, hyperparameters, training set size, and training duration, and are more precise than what is expected from existing domain adaptation theory. To complete the picture, we also investigate cases where the correlation is weaker, for instance some synthetic distribution shifts from CIFAR-10-C and the tissue classification dataset Camelyon17-WILDS. Finally, we provide a candidate theory based on a Gaussian data model that shows how changes in the data covariance arising from distribution shift can affect the observed correlations.

Several recent studies observed that when classification models are evaluated on two different data distributions, the models' accuracies on one distribution are approximately a linear function of their accuracies on another distribution. We offer an explanation for these observations based on two assumptions that can be assessed empirically: (1) certain events have similar probabilities under the two distributions; (2) the probability that a lower accuracy model correctly classifies a data point sampled from one distribution when a higher accuracy model classifies it incorrectly is small.

"It can be better!" was the feedback I got from my parents when I made tea for the first time. It was 1st January, I had taken many resolutions and learning to cook was one of them. I realised that two things are ruining my tea every time. First was the tea leaves and the other was sugar. Somehow I was never able to make a balance between them.

In this case, we would be interested used in biological and social sciences to predict events and to in identifying a segment of the population for which describe possible relationships between variables. When addressing a linear rule is highly predictive of the price of certain cars, the task of prediction, machine learning and statistics whereas this linear rule may not provide a good prediction commonly focus on capturing the vast majority of data, overall in the larger population. Let us imagine that for this occasionally ignoring a segment of the population as "outliers" data set, and for a target fraction of the population, we found or "noise," which could be helpful to better understand a simple rule that describes the subpopulation, along with the data. Previous work by Juba (2016) gave an algorithm its linear fit.