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 Statistical Learning


Leveraging Cross-Modal Neighbor Representation for Improved CLIP Classification

arXiv.org Artificial Intelligence

CLIP showcases exceptional cross-modal matching capabilities due to its training on image-text contrastive learning tasks. However, without specific optimization for unimodal scenarios, its performance in single-modality feature extraction might be suboptimal. Despite this, some studies have directly used CLIP's image encoder for tasks like few-shot classification, introducing a misalignment between its pre-training objectives and feature extraction methods. This inconsistency can diminish the quality of the image's feature representation, adversely affecting CLIP's effectiveness in target tasks. In this paper, we view text features as precise neighbors of image features in CLIP's space and present a novel CrOss-moDal nEighbor Representation(CODER) based on the distance structure between images and their neighbor texts. This feature extraction method aligns better with CLIP's pre-training objectives, thereby fully leveraging CLIP's robust cross-modal capabilities. The key to construct a high-quality CODER lies in how to create a vast amount of high-quality and diverse texts to match with images. We introduce the Auto Text Generator(ATG) to automatically generate the required texts in a data-free and training-free manner. We apply CODER to CLIP's zero-shot and few-shot image classification tasks. Experiment results across various datasets and models confirm CODER's effectiveness. Code is available at:https://github.com/YCaigogogo/CVPR24-CODER.


RE-RFME: Real-Estate RFME Model for customer segmentation

arXiv.org Artificial Intelligence

Marketing is one of the high-cost activities for any online platform. With the increase in the number of customers, it is crucial to understand customers based on their dynamic behaviors to design effective marketing strategies. Customer segmentation is a widely used approach to group customers into different categories and design the marketing strategy targeting each group individually. Therefore, in this paper, we propose an end-to-end pipeline RE-RFME for segmenting customers into 4 groups: high value, promising, need attention, and need activation. Concretely, we propose a novel RFME (Recency, Frequency, Monetary and Engagement) model to track behavioral features of customers and segment them into different categories. Finally, we train the K-means clustering algorithm to cluster the user into one of the 4 categories. We show the effectiveness of the proposed approach on real-world Housing.com datasets for both website and mobile application users.


Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes

arXiv.org Machine Learning

We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the Stein-Haff identity, an extension of the classical Stein's identity used in previous fingerprinting lemma arguments.


On the Rashomon ratio of infinite hypothesis sets

arXiv.org Machine Learning

Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.


Pseudo-Observations and Super Learner for the Estimation of the Restricted Mean Survival Time

arXiv.org Machine Learning

In the context of right-censored data, we study the problem of predicting the restricted time to event based on a set of covariates. Under a quadratic loss, this problem is equivalent to estimating the conditional Restricted Mean Survival Time (RMST). To that aim, we propose a flexible and easy-to-use ensemble algorithm that combines pseudo-observations and super learner. The classical theoretical results of the super learner are extended to right-censored data, using a new definition of pseudo-observations, the so-called split pseudo-observations. Simulation studies indicate that the split pseudo-observations and the standard pseudo-observations are similar even for small sample sizes. The method is applied to maintenance and colon cancer datasets, showing the interest of the method in practice, as compared to other prediction methods. We complement the predictions obtained from our method with our RMST-adapted risk measure, prediction intervals and variable importance measures developed in a previous work.


Any-Quantile Probabilistic Forecasting of Short-Term Electricity Demand

arXiv.org Machine Learning

Power systems operate under uncertainty originating from multiple factors that are impossible to account for deterministically. Distributional forecasting is used to control and mitigate risks associated with this uncertainty. Recent progress in deep learning has helped to significantly improve the accuracy of point forecasts, while accurate distributional forecasting still presents a significant challenge. In this paper, we propose a novel general approach for distributional forecasting capable of predicting arbitrary quantiles. We show that our general approach can be seamlessly applied to two distinct neural architectures leading to the state-of-the-art distributional forecasting results in the context of short-term electricity demand forecasting task. We empirically validate our method on 35 hourly electricity demand time-series for European countries. Our code is available here: https://github.com/boreshkinai/any-quantile.


Conformal Prediction with Learned Features

arXiv.org Machine Learning

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research has considered relaxations of full conditional guarantees, relying on some predefined uncertainty structures. Departing from this line of thinking, we propose Partition Learning Conformal Prediction (PLCP), a framework to improve conditional validity of prediction sets through learning uncertainty-guided features from the calibration data. We implement PLCP efficiently with alternating gradient descent, utilizing off-the-shelf machine learning models. We further analyze PLCP theoretically and provide conditional guarantees for infinite and finite sample sizes. Finally, our experimental results over four real-world and synthetic datasets show the superior performance of PLCP compared to state-of-the-art methods in terms of coverage and length in both classification and regression scenarios.


Online Policy Learning and Inference by Matrix Completion

arXiv.org Machine Learning

Making online decisions can be challenging when features are sparse and orthogonal to historical ones, especially when the optimal policy is learned through collaborative filtering. We formulate the problem as a matrix completion bandit (MCB), where the expected reward under each arm is characterized by an unknown low-rank matrix. The $\epsilon$-greedy bandit and the online gradient descent algorithm are explored. Policy learning and regret performance are studied under a specific schedule for exploration probabilities and step sizes. A faster decaying exploration probability yields smaller regret but learns the optimal policy less accurately. We investigate an online debiasing method based on inverse propensity weighting (IPW) and a general framework for online policy inference. The IPW-based estimators are asymptotically normal under mild arm-optimality conditions. Numerical simulations corroborate our theoretical findings. Our methods are applied to the San Francisco parking pricing project data, revealing intriguing discoveries and outperforming the benchmark policy.


Low-rank Matrix Bandits with Heavy-tailed Rewards

arXiv.org Machine Learning

In stochastic low-rank matrix bandit, the expected reward of an arm is equal to the inner product between its feature matrix and some unknown $d_1$ by $d_2$ low-rank parameter matrix $\Theta^*$ with rank $r \ll d_1\wedge d_2$. While all prior studies assume the payoffs are mixed with sub-Gaussian noises, in this work we loosen this strict assumption and consider the new problem of \underline{low}-rank matrix bandit with \underline{h}eavy-\underline{t}ailed \underline{r}ewards (LowHTR), where the rewards only have finite $(1+\delta)$ moment for some $\delta \in (0,1]$. By utilizing the truncation on observed payoffs and the dynamic exploration, we propose a novel algorithm called LOTUS attaining the regret bound of order $\tilde O(d^\frac{3}{2}r^\frac{1}{2}T^\frac{1}{1+\delta}/\tilde{D}_{rr})$ without knowing $T$, which matches the state-of-the-art regret bound under sub-Gaussian noises~\citep{lu2021low,kang2022efficient} with $\delta = 1$. Moreover, we establish a lower bound of the order $\Omega(d^\frac{\delta}{1+\delta} r^\frac{\delta}{1+\delta} T^\frac{1}{1+\delta}) = \Omega(T^\frac{1}{1+\delta})$ for LowHTR, which indicates our LOTUS is nearly optimal in the order of $T$. In addition, we improve LOTUS so that it does not require knowledge of the rank $r$ with $\tilde O(dr^\frac{3}{2}T^\frac{1+\delta}{1+2\delta})$ regret bound, and it is efficient under the high-dimensional scenario. We also conduct simulations to demonstrate the practical superiority of our algorithm.


Conformal Ranked Retrieval

arXiv.org Machine Learning

Ranked retrieval refers to the process of retrieving and ranking documents from a document repository based on their relevance to a user's query. As the core component in Information Retrieval (IR) systems, its goal is to present the most relevant documents at the top of the search results list, making it easier for users to find the information they seek (Baeza-Yates and Ribeiro-Neto, 1999). Over the years, ranked retrieval techniques have been successfully applied to many real-life problems, including web search engines, recommendation systems, and question-and-answer platforms, significantly impacting our daily lives. While ranked retrieval algorithms have been extensively studied in both academia and industry, considering the uncertainty in their predictions is a relatively new challenge. As we increasingly rely on search engines for answers to a wide variety of questions, it becomes crucial to evaluate the reliability of these retrieved answers. Therefore, it is important to quantify the uncertainty of the results, determining whether they encompass all the desired documents and whether these documents are ranked in a reasonable order. The challenges, however, lie in measuring uncertainty for ranked retrieval algorithms and developing methodologies to control this uncertainty. This is particularly challenging due to the complexity of ranked retrieval systems, which typically consist of multiple stages, each with different optimization goals.