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Generative large language models (LLMs), e.g., ChatGPT, have demonstrated remarkable proficiency across several NLP tasks such as machine translation, question answering, text summarization, and natural language understanding. Recent research has shown that utilizing ChatGPT for assessing the quality of machine translation (MT) achieves state-of-the-art performance at the system level but performs poorly at the segment level. To further improve the performance of LLMs on MT quality assessment, we conducted an investigation into several prompting methods. Our results indicate that by combining Chain-of-Thoughts and Error Analysis, a new prompting method called \textbf{\texttt{Error Analysis Prompting}}, LLMs like ChatGPT can \textit{generate human-like MT evaluations at both the system and segment level}. Additionally, we discovered some limitations of ChatGPT as an MT evaluator, such as unstable scoring and biases when provided with multiple translations in a single query. Our findings aim to provide a preliminary experience for appropriately evaluating translation quality on ChatGPT while offering a variety of tricks in designing prompts for in-context learning. We anticipate that this report will shed new light on advancing the field of translation evaluation with LLMs by enhancing both the accuracy and reliability of metrics. The project can be found in \url{//github.com/Coldmist-Lu/ErrorAnalysis_Prompt}.

Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progression described by a multistate model, the pseudo-value regression technique has gained popularity in time-to-event data analysis. We seek to answer the question: "How to apply pseudo-value regression to clustered time-to-event data when cluster size is informative?" ICS adjustment by the reweighting method can be performed in two steps; estimation of marginal functions of the multistate model and fitting the estimating equations based on pseudo-value responses, leading to four possible strategies. We present theoretical arguments and thorough simulation experiments to ascertain the correct strategy for adjusting for ICS. A further extension of our methodology is implemented to include informativeness induced by the intra-cluster group size. We demonstrate the methods in two real-world applications: (i) to determine predictors of tooth survival in a periodontal study, and (ii) to identify indicators of ambulatory recovery in spinal cord injury patients who participated in locomotor-training rehabilitation.

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of clusters. On the other hand, probabilistic model-based clustering techniques often fail to scale and devising algorithms that are able to effectively explore the posterior space is an open problem. Based on recent developments in Bayesian distance-based clustering, we propose a hybrid solution that entails defining a likelihood on pairwise distances between observations. The novelty of the approach consists in including both cohesion and repulsion terms in the likelihood, which allows for cluster identifiability. This implies that clusters are composed of objects which have small "dissimilarities" among themselves (cohesion) and similar dissimilarities to observations in other clusters (repulsion). We show how this modelling strategy has interesting connection with existing proposals in the literature as well as a decision-theoretic interpretation. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in a simulation study and an application in digital numismatics.

The Internet has turned the entire world into a small village;this is because it has made it possible to share millions of images and videos. However, sending and receiving a huge amount of data is considered to be a main challenge. To address this issue, a new algorithm is required to reduce image bits and represent the data in a compressed form. Nevertheless, image compression is an important application for transferring large files and images. This requires appropriate and efficient transfers in this field to achieve the task and reach the best results. In this work, we propose a new algorithm based on discrete Hermite wavelets transformation (DHWT) that shows the efficiency and quality of the color images. By compressing the color image, this method analyzes it and divides it into approximate coefficients and detail coefficients after adding the wavelets into MATLAB. With Multi-Resolution Analyses (MRA), the appropriate filter is derived, and the mathematical aspects prove to be validated by testing a new filter and performing its operation. After the decomposition of the rows and upon the process of the reconstruction, taking the inverse of the filter and dealing with the columns of the matrix, the original matrix is improved by measuring the parameters of the image to achieve the best quality of the resulting image, such as the peak signal-to-noise ratio (PSNR), compression ratio (CR), bits per pixel (BPP), and mean square error (MSE).

Top-N recommendation aims to recommend each consumer a small set of N items from a large collection of items, and its accuracy is one of the most common indexes to evaluate the performance of a recommendation system. While a large number of algorithms are proposed to push the Top-N accuracy by learning the user preference from their history purchase data, a predictability question is naturally raised - whether there is an upper limit of such Top-N accuracy. This work investigates such predictability by studying the degree of regularity from a specific set of user behavior data. Quantifying the predictability of Top-N recommendations requires simultaneously quantifying the limits on the accuracy of the N behaviors with the highest probability. This greatly increases the difficulty of the problem. To achieve this, we firstly excavate the associations among N behaviors with the highest probability and describe the user behavior distribution based on the information theory. Then, we adopt the Fano inequality to scale and obtain the Top-N predictability. Extensive experiments are conducted on the real-world data where significant improvements are observed compared to the state-of-the-art methods. We have not only completed the predictability calculation for N targets but also obtained predictability that is much closer to the true value than existing methods. We expect our results to assist these research areas where the quantitative requirement of Top-N predictability is required.

Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, $X$ can be "thinned" into independent random variables $X^{(1)}, \ldots, X^{(K)}$, such that $X = \sum_{k=1}^K X^{(k)}$. In this paper, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct $X$. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families.

This study proposes a simulation framework of procurement operations in the container logistics industry that can support the development of dynamic procurement strategies. The idea is inspired by the success of Passenger Origin-Destination Simulator (PODS) in the field of airline revenue management. By and large, research in procurement has focused on the optimisation of purchasing decisions, i.e., when-to-order and supplier selection, but a principled approach to procurement operations is lacking. We fill this gap by developing a probabilistic model of a procurement system. A discrete-event simulation logic is used to drive the evolution of the system. In a small case study, we use the simulation to deliver insights by comparing different supplier selection policies in a dynamic spot market environment. Policies based on contextual multi-armed bandits are seen to be robust to limited access to the information that determines the distribution of the outcome. This paper provides a pool of modelling ideas for simulation and observational studies. Moreover, the probabilistic formulation paves the way for advanced machine learning techniques and data-driven optimisation in procurement.

We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this, almost no hardness results with respect to the polynomial hierarchy are known. In this work, we examine the hardness of robust two-stage adjustable and robust recoverable optimization with budgeted uncertainty sets. Our main technical contribution is the introduction of a technique tailored to prove $\Sigma^p_3$-hardness of such problems. We highlight a difference between continuous and discrete budgeted uncertainty: In the discrete case, indeed a wide range of problems becomes complete for the third stage of the polynomial hierarchy; in particular, this applies to the TSP, independent set, and vertex cover problems. However, in the continuous case this does not happen and problems remain in the first stage of the hierarchy. Finally, if we allow the uncertainty to not only affect the objective, but also multiple constraints, then this distinction disappears and even in the continuous case we encounter hardness for the third stage of the hierarchy. This shows that even robust problems which are already NP-complete can still exhibit a significant computational difference between column-wise and row-wise uncertainty.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.