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Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many real-world scenarios, controlling certain query variables may incur costs. Therefore, the learner needs to balance the selection of informative subsets for targeted learning against leaving some variables to be randomly sampled to minimize costs. This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS). While the goal of BOCVS is to identify the optimal solution with minimal cost, previous works have only guaranteed finding the optimal solution without considering the total costs incurred. Moreover, these works assume precise knowledge of the cost for each subset, which is often unrealistic. In this paper, we propose a novel algorithm for the extension of the BOCVS problem with random and unknown costs that separates the process into exploration and exploitation phases. The exploration phase will filter out low-quality variable subsets, while the exploitation phase will leverage high-quality ones. Furthermore, we theoretically demonstrate that our algorithm achieves a sub-linear rate in both quality regret and cost regret, addressing the objective of the BOCVS problem more effectively than previous analyses. Finally, we show that our proposed algorithm outperforms comparable baselines across a wide range of benchmarks.

This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C($\alpha$) style tests are locally regular under mild conditions, including in cases where locally regular estimators do not exist, such as models which are (semiparametrically) weakly identified. I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the non-regular case and generalise classical power bounds to this case. I give conditions under which these power bounds are attained by the proposed C($\alpha$) style tests. The application of the theory to a single index model and an instrumental variables model is worked out in detail.

We introduce SONO, a novel method leveraging Second-Order Neural Ordinary Differential Equations (Second-Order NODEs) to enhance cross-modal few-shot learning. By employing a simple yet effective architecture consisting of a Second-Order NODEs model paired with a cross-modal classifier, SONO addresses the significant challenge of overfitting, which is common in few-shot scenarios due to limited training examples. Our second-order approach can approximate a broader class of functions, enhancing the model's expressive power and feature generalization capabilities. We initialize our cross-modal classifier with text embeddings derived from class-relevant prompts, streamlining training efficiency by avoiding the need for frequent text encoder processing. Additionally, we utilize text-based image augmentation, exploiting CLIP's robust image-text correlation to enrich training data significantly. Extensive experiments across multiple datasets demonstrate that SONO outperforms existing state-of-the-art methods in few-shot learning performance.

A recently proposed scheme utilizing local noise addition and matrix masking enables data collection while protecting individual privacy from all parties, including the central data manager. Statistical analysis of such privacy-preserved data is particularly challenging for nonlinear models like logistic regression. By leveraging a relationship between logistic regression and linear regression estimators, we propose the first valid statistical analysis method for logistic regression under this setting. Theoretical analysis of the proposed estimators confirmed its validity under an asymptotic framework with increasing noise magnitude to account for strict privacy requirements. Simulations and real data analyses demonstrate the superiority of the proposed estimators over naive logistic regression methods on privacy-preserved data sets.

We propose a highly flexible distributional copula regression model for bivariate time-to-event data in the presence of right-censoring. The joint survival function of the response is constructed using parametric copulas, allowing for a separate specification of the dependence structure between the time-to-event outcome variables and their respective marginal survival distributions. The latter are specified using well-known parametric distributions such as the log-Normal, log-Logistic (proportional odds model), or Weibull (proportional hazards model) distributions. Hence, the marginal univariate event times can be specified as parametric (also known as Accelerated Failure Time, AFT) models. Embedding our model into the class of generalized additive models for location, scale and shape, possibly all distribution parameters of the joint survival function can depend on covariates. We develop a component-wise gradient-based boosting algorithm for estimation. This way, our approach is able to conduct data-driven variable selection. To the best of our knowledge, this is the first implementation of multivariate AFT models via distributional copula regression with automatic variable selection via statistical boosting. A special merit of our approach is that it works for high-dimensional (p>>n) settings. We illustrate the practical potential of our method on a high-dimensional application related to semi-competing risks responses in ovarian cancer. All of our methods are implemented in the open source statistical software R as add-on functions of the package gamboostLSS.

We argue that the Declarative Self-improving Python (DSPy) optimizers are a way to align the large language model (LLM) prompts and their evaluations to the human annotations. We present a comparative analysis of five teleprompter algorithms, namely, Cooperative Prompt Optimization (COPRO), Multi-Stage Instruction Prompt Optimization (MIPRO), BootstrapFewShot, BootstrapFewShot with Optuna, and K-Nearest Neighbor Few Shot, within the DSPy framework with respect to their ability to align with human evaluations. As a concrete example, we focus on optimizing the prompt to align hallucination detection (using LLM as a judge) to human annotated ground truth labels for a publicly available benchmark dataset. Our experiments demonstrate that optimized prompts can outperform various benchmark methods to detect hallucination, and certain telemprompters outperform the others in at least these experiments.

The recent development of foundation models for monocular depth estimation such as Depth Anything paved the way to zero-shot monocular depth estimation. Since it returns an affine-invariant disparity map, the favored technique to recover the metric depth consists in fine-tuning the model. However, this stage is costly to perform because of the training but also due to the creation of the dataset. It must contain images captured by the camera that will be used at test time and the corresponding ground truth. Moreover, the fine-tuning may also degrade the generalizing capacity of the original model. Instead, we propose in this paper a new method to rescale Depth Anything predictions using 3D points provided by low-cost sensors or techniques such as low-resolution LiDAR, stereo camera, structure-from-motion where poses are given by an IMU. Thus, this approach avoids fine-tuning and preserves the generalizing power of the original depth estimation model while being robust to the noise of the sensor or of the depth model. Our experiments highlight improvements relative to other metric depth estimation methods and competitive results compared to fine-tuned approaches. Code available at //gitlab.ensta.fr/ssh/monocular-depth-rescaling.

This paper provides a compact method to lift the free exponential construction of Mellies-Tabareau-Tasson over the Hyland-Schalk double glueing for orthogonality categories. A condition ``reciprocity of orthogonality'' is presented simply enough to lift the free exponential over the double glueing in terms of the orthogonality. Our general method applies to the monoidal category TsK of the s-finite transition kernels with countable biproducts. We show (i) TsK^op has the free exponential, which is shown to be describable in terms of measure theory. (ii) The s-finite transition kernels have an orthogonality between measures and measurable functions in terms of Lebesgue integrals. The orthogonality is reciprocal, hence the free exponential of (i) lifts to the orthogonality category O_I(TsK^op), which subsumes Ehrhard et al's probabilistic coherent spaces as a full subcategory of countable measurable spaces. To lift the free exponential, the measure-theoretic uniform convergence theorem commuting Lebesgue integral and limit plays a crucial role as well as Fubini-Tonelli theorem for double integral in s-finiteness. Our measure-theoretic orthogonality is considered as a continuous version of the orthogonality of the probabilistic coherent spaces for linear logic, and in particular provides a two layered decomposition of Crubille et al's direct free exponential for these spaces.

In this paper, a novel classification algorithm that is based on Data Importance (DI) reformatting and Genetic Algorithms (GA) named GADIC is proposed to overcome the issues related to the nature of data which may hinder the performance of the Machine Learning (ML) classifiers. GADIC comprises three phases which are data reformatting phase which depends on DI concept, training phase where GA is applied on the reformatted training dataset, and testing phase where the instances of the reformatted testing dataset are being averaged based on similar instances in the training dataset. GADIC is an approach that utilizes the exiting ML classifiers with involvement of data reformatting, using GA to tune the inputs, and averaging the similar instances to the unknown instance. The averaging of the instances becomes the unknown instance to be classified in the stage of testing. GADIC has been tested on five existing ML classifiers which are Support Vector Machine (SVM), K-Nearest Neighbour (KNN), Logistic Regression (LR), Decision Tree (DT), and Na\"ive Bayes (NB). All were evaluated using seven open-source UCI ML repository and Kaggle datasets which are Cleveland heart disease, Indian liver patient, Pima Indian diabetes, employee future prediction, telecom churn prediction, bank customer churn, and tech students. In terms of accuracy, the results showed that, with the exception of approximately 1% decrease in the accuracy of NB classifier in Cleveland heart disease dataset, GADIC significantly enhanced the performance of most ML classifiers using various datasets. In addition, KNN with GADIC showed the greatest performance gain when compared with other ML classifiers with GADIC followed by SVM while LR had the lowest improvement. The lowest average improvement that GADIC could achieve is 5.96%, whereas the maximum average improvement reached 16.79%.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.