How can we precisely estimate a large language model's (LLM) accuracy on questions belonging to a specific topic within a larger question-answering dataset? The standard direct estimator, which averages the model's accuracy on the questions in each subgroup, may exhibit high variance for subgroups (topics) with small sample sizes. Synthetic regression modeling, which leverages the model's accuracy on questions about other topics, may yield biased estimates that are too unreliable for large subgroups. We prescribe a simple yet effective solution: an empirical Bayes (EB) estimator that balances direct and regression estimates for each subgroup separately, improving the precision of subgroup-level estimates of model performance. Our experiments on multiple datasets show that this approach consistently provides more precise estimates of the LLM performance compared to the direct and regression approaches, achieving substantial reductions in the mean squared error. Confidence intervals for EB estimates also have near-nominal coverage and are narrower compared to those for the direct estimator. Additional experiments on tabular and vision data validate the benefits of this EB approach.

Decision trees are powerful for predictive modeling but often suffer from high variance when modeling continuous relationships. While algorithms like Multivariate Adaptive Regression Splines (MARS) excel at capturing such continuous relationships, they perform poorly when modeling discontinuities. To address the limitations of both approaches, we introduce Spline-based Multivariate Adaptive Regression Trees (SMART), which uses a decision tree to identify subsets of data with distinct continuous relationships and then leverages MARS to fit these relationships independently. Unlike other methods that rely on the tree structure to model interaction and higher-order terms, SMART leverages MARS's native ability to handle these terms, allowing the tree to focus solely on identifying discontinuities in the relationship. We test SMART on various datasets, demonstrating its improvement over state-of-the-art methods in such cases. Additionally, we provide an open-source implementation of our method to be used by practitioners.

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression performance after being applied to the covariates. More precisely, we consider disjoint groups of independent random projections, apply a base regression method after each projection, and retain the projection in each group based on the empirical performance. We aggregate the selected projections by taking the singular value decomposition of their empirical average and then output the leading order singular vectors. A particularly appealing aspect of our approach is that the singular values provide a measure of the relative importance of the corresponding projection directions, which can be used to select the final projection dimension. We investigate in detail (and provide default recommendations for) various aspects of our general framework, including the projection distribution and the base regression method, as well as the number of random projections used. Additionally, we investigate the possibility of further reducing the dimension by applying our algorithm twice in cases where projection dimension recommended in the initial application is too large. Our theoretical results show that the error of our algorithm stabilises as the number of groups of projections increases. We demonstrate the excellent empirical performance of our proposal in a large numerical study using simulated and real data.

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition.

One recent research demonstrated successful application of the label alignment property for unsupervised domain adaptation in a linear regression settings. Instead of regularizing representation learning to be domain invariant, the research proposed to regularize the linear regression model to align with the top singular vectors of the data matrix from the target domain. In this work we expand upon this idea and generalize it to the case of deep learning, where we derive an alternative formulation of the original adaptation algorithm exploiting label alignment suitable for deep neural network. We also perform experiments to demonstrate that our approach achieves comparable performance to mainstream unsupervised domain adaptation methods while having stabler convergence.

The research investigates how the application of a machine-learning random forest model improves the accuracy and precision of a Delphi model. The context of the research is Azerbaijani SMEs and the data for the study has been obtained from a financial institution which had gathered it from the enterprises (as there is no public data on local SMEs, it was not practical to verify the data independently). The research used accuracy, precision, recall and F-1 scores for both models to compare them and run the algorithms in Python. The findings showed that accuracy, precision, recall and F- 1 all improve considerably (from 0.69 to 0.83, from 0.65 to 0.81, from 0.56 to 0.77 and from 0.58 to 0.79, respectively). The implications are that by applying AI models in credit risk modeling, financial institutions can improve the accuracy of identifying potential defaulters which would reduce their credit risk. In addition, an unfair rejection of credit access for SMEs would also go down having a significant contribution to an economic growth in the economy. Finally, such ethical issues as transparency of algorithms and biases in historical data should be taken on board while making decisions based on AI algorithms in order to reduce mechanical dependence on algorithms that cannot be justified in practice.

We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.

This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.

We present the first efficient and provably consistent estimator for the robust regression problem. The area of robust learning and optimization has generated a significant amount of interest in the learning and statistics communities in recent years owing to its applicability in scenarios with corrupted data, as well as in handling model mis-specifications. In particular, special interest has been devoted to the fundamental problem of robust linear regression where estimators that can tolerate corruption in up to a constant fraction of the response variables are widely studied. Surprisingly however, to this date, we are not aware of a polynomial time estimator that offers a consistent estimate in the presence of dense, unbounded corruptions. In this work we present such an estimator, called CRR. This solves an open problem put forward in the work of [3]. Our consistency analysis requires a novel two-stage proof technique involving a careful analysis of the stability of ordered lists which may be of independent interest.