We propose ECPv2, a scalable and theoretically grounded algorithm for global optimization of Lipschitz-continuous functions with unknown Lipschitz constants. Building on the Every Call is Precious (ECP) framework, which ensures that each accepted function evaluation is potentially informative, ECPv2 addresses key limitations of ECP, including high computational cost and overly conservative early behavior. ECPv2 introduces three innovations: (i) an adaptive lower bound to avoid vacuous acceptance regions, (ii) a Worst-m memory mechanism that restricts comparisons to a fixed-size subset of past evaluations, and (iii) a fixed random projection to accelerate distance computations in high dimensions. We theoretically show that ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability. We further empirically validate these findings through extensive experiments and ablation studies. Using principled hyperparameter settings, we evaluate ECPv2 across a wide range of high-dimensional, non-convex optimization problems. Across benchmarks, ECPv2 consistently matches or outperforms state-of-the-art optimizers, while significantly reducing wall-clock time.

Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that belong to overlapping regions of the two class distributions or for data outside the distributions (out-of-distribution data). Therefore, conventional classifiers should not be applied in high-risk fields where classification results can have significant consequences. In order to address this issue, it is necessary to quantify uncertainty and adopt decision-making approaches that take it into account. Many methods have been proposed for this purpose; however, implementing these methods often requires performing resampling, improving the structure or performance of models, and optimizing the thresholds of classifiers. We propose a new decision-making approach using two types of hypothesis testing. This method is capable of detecting ambiguous data that belong to the overlapping regions of two class distributions, as well as out-of-distribution data that are not included in the training data distribution. In addition, we quantify uncertainty using the empirical distribution of feature values derived from the training data obtained through the trained model. The classification threshold is determined by the $\alpha$-quantile and ($1-\alpha$)-quantile, where the significance level $\alpha$ is set according to each specific situation.

Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.

Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly, in machine learning, practitioners are often interested in the population performance of the model that performs best empirically. However, cherry-picking the best candidate leads to the winner's curse: the observed performance for the winner is biased upwards, rendering conclusions based on standard measures of uncertainty invalid. We introduce the zoom correction, a novel approach for valid inference on the winner. Our method is flexible: it can be employed in both parametric and nonparametric settings, can handle arbitrary dependencies between candidates, and automatically adapts to the level of selection bias. The method easily extends to important related problems, such as inference on the top k winners, inference on the value and identity of the population winner, and inference on "near-winners."

This paper introduces a novel approach for click-through rate (CTR) prediction within industrial recommender systems, addressing the inherent challenges of numerical imbalance and geometric asymmetry. These challenges stem from imbalanced datasets, where positive (click) instances occur less frequently than negatives (non-clicks), and geometrically asymmetric distributions, where positive samples exhibit visually coherent patterns while negatives demonstrate greater diversity. To address these challenges, we have used a deep neural network classifier that uses the polyhedral conic functions. This classifier is similar to the one-class classifiers in spirit and it returns compact polyhedral acceptance regions to separate the positive class samples from the negative samples that have diverse distributions. Extensive experiments have been conducted to test the proposed approach using state-of-the-art (SOTA) CTR prediction models on four public datasets, namely Criteo, Avazu, MovieLens and Frappe. The experimental evaluations highlight the superiority of our proposed approach over Binary Cross Entropy (BCE) Loss, which is widely used in CTR prediction tasks.

Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness revolve around efforts to clean or curate training data, with post-hoc statistical evaluation of the fairness of the model on evaluation data. In contrast, we propose techniques to \emph{prove} fairness using recently developed formal methods that verify properties of neural network models.Beyond the strength of guarantee implied by a formal proof, our methods have the advantage that we do not need explicit training or evaluation data (which is often proprietary) in order to analyze a given trained model. In experiments on two familiar datasets in the fairness literature (COMPAS and ADULTS), we show that through proper training, we can reduce unfairness by an average of 65.4\% at a cost of less than 1\% in AUC score.

In multicategory classification, traditional methods return a single class label as the prediction without a confidence measure attached. For points near the classification boundary where the classes overlap, these methods may misclassify with high probability. As classification and machine learning in general have played a more and more significant role in high stake domains, these mistakes can incur severe consequences. To avoid making mistakes when they are likely to happen, set-valued classification methods have emerged (Herbei and Wegkamp, 2006; Shafer and Vovk, 2008; Dümbgen et al., 2008; Denis and Hebiri, 2017; Wang and Qiao, 2018; Zhang et al., 2018; Sadinle et al., 2019). A set-valued classifier may return multiple class labels as the prediction for each observation. Specifically, those near the boundary between classes may receive multiple labels as the prediction. Herbei and Wegkamp (2006), Bartlett and Wegkamp (2008), Ramaswamy et al. (2015) and Zhang et al. (2018) proposed and developed Classification with a Reject Option (CRO) by training a classifier and a rejector at the same time. A rejector determines when to refuse to make a classification for ambiguous points (i.e.

When it comes to statistics in machine learning, a common approach to accept or reject a null hypothesis is to check for the p-values and give a result without really having an idea of what goes on in the background. Without getting into any kind of fancy jargons or mathematical technicalities, this article attempts to sum up the intuition behind statistics using some real life examples especially for people from a non-statistics background. Why do we need hypothesis testing? But what if suddenly, Dunkin' happens to shut down because Krispe Kreme claims the weight of their donuts is less than what Dunkin' claims. How do we choose sides?