Aggregating Data for Optimal and Private Learning

Multiple Instance Regression (MIR) and Learning from Label Proportions (LLP) are learning frameworks arising in many applications, where the training data is partitioned into disjoint sets or bags, and only an aggregate label i.e., bag-label for each bag is available to the learner. In the case of MIR, the bag-label is the label of an undisclosed instance from the bag, while in LLP, the bag-label is the mean of the bag's labels. In this paper, we study for various loss functions in MIR and LLP, what is the optimal way to partition the dataset into bags such that the utility for downstream tasks like linear regression is maximized. We theoretically provide utility guarantees, and show that in each case, the optimal bagging strategy (approximately) reduces to finding an optimal clustering of the feature vectors or the labels with respect to natural objectives such as $k$-means. We also show that our bagging mechanisms can be made label-differentially private, incurring an additional utility error. We then generalize our results to the setting of Generalized Linear Models (GLMs). Finally, we experimentally validate our theoretical results.

Learning from Label Proportions and Covariate-shifted Instances

In many applications, especially due to lack of supervision or privacy concerns, the training data is grouped into bags of instances (feature-vectors) and for each bag we have only an aggregate label derived from the instance-labels in the bag. In learning from label proportions (LLP) the aggregate label is the average of the instance-labels in a bag, and a significant body of work has focused on training models in the LLP setting to predict instance-labels. In practice however, the training data may have fully supervised albeit covariate-shifted source data, along with the usual target data with bag-labels, and we wish to train a good instance-level predictor on the target domain. We call this the covariate-shifted hybrid LLP problem. Fully supervised covariate shifted data often has useful training signals and the goal is to leverage them for better predictive performance in the hybrid LLP setting. To achieve this, we develop methods for hybrid LLP which naturally incorporate the target bag-labels along with the source instance-labels, in the domain adaptation framework. Apart from proving theoretical guarantees bounding the target generalization error, we also conduct experiments on several publicly available datasets showing that our methods outperform LLP and domain adaptation baselines as well techniques from previous related work.

Preserving Expert-Level Privacy in Offline Reinforcement Learning

The offline reinforcement learning (RL) problem aims to learn an optimal policy from historical data collected by one or more behavioural policies (experts) by interacting with an environment. However, the individual experts may be privacy-sensitive in that the learnt policy may retain information about their precise choices. In some domains like personalized retrieval, advertising and healthcare, the expert choices are considered sensitive data. To provably protect the privacy of such experts, we propose a novel consensus-based expert-level differentially private offline RL training approach compatible with any existing offline RL algorithm. We prove rigorous differential privacy guarantees, while maintaining strong empirical performance. Unlike existing work in differentially private RL, we supplement the theory with proof-of-concept experiments on classic RL environments featuring large continuous state spaces, demonstrating substantial improvements over a natural baseline across multiple tasks.

FRACTAL: Fine-Grained Scoring from Aggregate Text Labels

Large language models (LLMs) are being increasingly tuned to power complex generation tasks such as writing, fact-seeking, querying and reasoning. Traditionally, human or model feedback for evaluating and further tuning LLM performance has been provided at the response level, enabling faster and more cost-effective assessments. However, recent works (Amplayo et al. [2022], Wu et al. [2023]) indicate that sentence-level labels may provide more accurate and interpretable feedback for LLM optimization. In this work, we introduce methods to disaggregate response-level labels into sentence-level (pseudo-)labels. Our approach leverages multiple instance learning (MIL) and learning from label proportions (LLP) techniques in conjunction with prior information (e.g., document-sentence cosine similarity) to train a specialized model for sentence-level scoring. We also employ techniques which use model predictions to pseudo-label the train-set at the sentence-level for model training to further improve performance. We conduct extensive evaluations of our methods across six datasets and four tasks: retrieval, question answering, summarization, and math reasoning. Our results demonstrate improved performance compared to multiple baselines across most of these tasks. Our work is the first to develop response-level feedback to sentence-level scoring techniques, leveraging sentence-level prior information, along with comprehensive evaluations on multiple tasks as well as end-to-end finetuning evaluation showing performance comparable to a model trained on fine-grained human annotated labels.

Label Differential Privacy via Aggregation

In many real-world applications, in particular due to recent developments in the privacy landscape, training data may be aggregated to preserve the privacy of sensitive training labels. In the learning from label proportions (LLP) framework, the dataset is partitioned into bags of feature-vectors which are available only with the sum of the labels per bag. A further restriction, which we call learning from bag aggregates (LBA) is where instead of individual feature-vectors, only the (possibly weighted) sum of the feature-vectors per bag is available. We study whether such aggregation techniques can provide privacy guarantees under the notion of label differential privacy (label-DP) previously studied in for e.g. [Chaudhuri-Hsu'11, Ghazi et al.'21, Esfandiari et al.'22]. It is easily seen that naive LBA and LLP do not provide label-DP. Our main result however, shows that weighted LBA using iid Gaussian weights with $m$ randomly sampled disjoint $k$-sized bags is in fact $(\varepsilon, \delta)$-label-DP for any $\varepsilon > 0$ with $\delta \approx \exp(-\Omega(\sqrt{k}))$ assuming a lower bound on the linear-mse regression loss. Further, this preserves the optimum over linear mse-regressors of bounded norm to within $(1 \pm o(1))$-factor w.p. $\approx 1 - \exp(-\Omega(m))$. We emphasize that no additive label noise is required. The analogous weighted-LLP does not however admit label-DP. Nevertheless, we show that if additive $N(0, 1)$ noise can be added to any constant fraction of the instance labels, then the noisy weighted-LLP admits similar label-DP guarantees without assumptions on the dataset, while preserving the utility of Lipschitz-bounded neural mse-regression tasks. Our work is the first to demonstrate that label-DP can be achieved by randomly weighted aggregation for regression tasks, using no or little additive noise.

PAC Learning Linear Thresholds from Label Proportions

Learning from label proportions (LLP) is a generalization of supervised learning in which the training data is available as sets or bags of feature-vectors (instances) along with the average instance-label of each bag. The goal is to train a good instance classifier. While most previous works on LLP have focused on training models on such training data, computational learnability of LLP was only recently explored by [Saket'21, Saket'22] who showed worst case intractability of properly learning linear threshold functions (LTFs) from label proportions. However, their work did not rule out efficient algorithms for this problem on natural distributions. In this work we show that it is indeed possible to efficiently learn LTFs using LTFs when given access to random bags of some label proportion in which feature-vectors are, conditioned on their labels, independently sampled from a Gaussian distribution $N(\mathbf{\mu}, \mathbf{\Sigma})$. Our work shows that a certain matrix -- formed using covariances of the differences of feature-vectors sampled from the bags with and without replacement -- necessarily has its principal component, after a transformation, in the direction of the normal vector of the LTF. Our algorithm estimates the means and covariance matrices using subgaussian concentration bounds which we show can be applied to efficiently sample bags for approximating the normal direction. Using this in conjunction with novel generalization error bounds in the bag setting, we show that a low error hypothesis LTF can be identified. For some special cases of the $N(\mathbf{0}, \mathbf{I})$ distribution we provide a simpler mean estimation based algorithm. We include an experimental evaluation of our learning algorithms along with a comparison with those of [Saket'21, Saket'22] and random LTFs, demonstrating the effectiveness of our techniques.

LLP-Bench: A Large Scale Tabular Benchmark for Learning from Label Proportions

In the task of Learning from Label Proportions (LLP), a model is trained on groups (a.k.a bags) of instances and their corresponding label proportions to predict labels for individual instances. LLP has been applied pre-dominantly on two types of datasets - image and tabular. In image LLP, bags of fixed size are created by randomly sampling instances from an underlying dataset. Bags created via this methodology are called random bags. Experimentation on Image LLP has been mostly on random bags on CIFAR-* and MNIST datasets. Despite being a very crucial task in privacy sensitive applications, tabular LLP does not yet have a open, large scale LLP benchmark. One of the unique properties of tabular LLP is the ability to create feature bags where all the instances in a bag have the same value for a given feature. It has been shown in prior research that feature bags are very common in practical, real world applications [Chen et. al '23, Saket et. al. '22]. In this paper, we address the lack of a open, large scale tabular benchmark. First we propose LLP-Bench, a suite of 56 LLP datasets (52 feature bag and 4 random bag datasets) created from the Criteo CTR prediction dataset consisting of 45 million instances. The 56 datasets represent diverse ways in which bags can be constructed from underlying tabular data. To the best of our knowledge, LLP-Bench is the first large scale tabular LLP benchmark with an extensive diversity in constituent datasets. Second, we propose four metrics that characterize and quantify the hardness of a LLP dataset. Using these four metrics we present deep analysis of the 56 datasets in LLP-Bench. Finally we present the performance of 9 SOTA and popular tabular LLP techniques on all the 56 datasets. To the best of our knowledge, our study consisting of more than 2500 experiments is the most extensive study of popular tabular LLP techniques in literature.

Learning from Label Proportions: Bootstrapping Supervised Learners via Belief Propagation

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

Improving Fairness-Accuracy tradeoff with few Test Samples under Covariate Shift

Covariate shift in the test data can significantly downgrade both the accuracy and the fairness performance of the model. Ensuring fairness across different sensitive groups in such settings is of paramount importance due to societal implications like criminal justice. We operate under the unsupervised regime where only a small set of unlabeled test samples along with a labeled training set is available. Towards this problem, we make three contributions. First is a novel composite weighted entropy based objective for prediction accuracy which is optimized along with a representation matching loss for fairness. We experimentally verify that optimizing with our loss formulation outperforms a number of state-of-the-art baselines in the pareto sense with respect to the fairness-accuracy tradeoff on several standard datasets. Our second contribution is a new setting we term Asymmetric Covariate Shift that, to the best of our knowledge, has not been studied before. Asymmetric covariate shift occurs when distribution of covariates of one group shifts significantly compared to the other groups and this happens when a dominant group is over-represented. While this setting is extremely challenging for current baselines, We show that our proposed method significantly outperforms them. Our third contribution is theoretical, where we show that our weighted entropy term along with prediction loss on the training set approximates test loss under covariate shift. Empirically and through formal sample complexity bounds, we show that this approximation to the unseen test loss does not depend on importance sampling variance which affects many other baselines.

BiPhone: Modeling Inter Language Phonetic Influences in Text

A large number of people are forced to use the Web in a language they have low literacy in due to technology asymmetries. Written text in the second language (L2) from such users often contains a large number of errors that are influenced by their native language (L1). We propose a method to mine phoneme confusions (sounds in L2 that an L1 speaker is likely to conflate) for pairs of L1 and L2. These confusions are then plugged into a generative model (Bi-Phone) for synthetically producing corrupted L2 text. Through human evaluations, we show that Bi-Phone generates plausible corruptions that differ across L1s and also have widespread coverage on the Web. We also corrupt the popular language understanding benchmark SuperGLUE with our technique (FunGLUE for Phonetically Noised GLUE) and show that SoTA language understating models perform poorly. We also introduce a new phoneme prediction pre-training task which helps byte models to recover performance close to SuperGLUE. Finally, we also release the FunGLUE benchmark to promote further research in phonetically robust language models. To the best of our knowledge, FunGLUE is the first benchmark to introduce L1-L2 interactions in text.