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The rapid advancement of Large Language Models (LLMs) highlights the urgent need for evolving evaluation methodologies that keep pace with improvements in language comprehension and information processing. However, traditional benchmarks, which are often static, fail to capture the continually changing information landscape, leading to a disparity between the perceived and actual effectiveness of LLMs in ever-changing real-world scenarios. Our study examines temporal generalization, which includes the ability to understand, predict, and generate text relevant to past, present, and future contexts, revealing significant temporal biases in LLMs. We propose an evaluation framework, for dynamically generating benchmarks from recent real-world predictions. Experiments demonstrate that LLMs struggle with temporal generalization, showing performance decline over time. These findings highlight the necessity for improved training and updating processes to enhance adaptability and reduce biases. Our code, dataset and benchmark are available at https://github.com/FreedomIntelligence/FreshBench., Comment: Preprint

Hierarchical text classification aims to categorize each document into a set of classes in a label taxonomy. Most earlier works focus on fully or semi-supervised methods that require a large amount of human annotated data which is costly and time-consuming to acquire. To alleviate human efforts, in this paper, we work on hierarchical text classification with the minimal amount of supervision: using the sole class name of each node as the only supervision. Recently, large language models (LLM) show competitive performance on various tasks through zero-shot prompting, but this method performs poorly in the hierarchical setting, because it is ineffective to include the large and structured label space in a prompt. On the other hand, previous weakly-supervised hierarchical text classification methods only utilize the raw taxonomy skeleton and ignore the rich information hidden in the text corpus that can serve as additional class-indicative features. To tackle the above challenges, we propose TELEClass, Taxonomy Enrichment and LLM-Enhanced weakly-supervised hierarchical text Classification, which (1) automatically enriches the label taxonomy with class-indicative terms to facilitate classifier training and (2) utilizes LLMs for both data annotation and creation tailored for the hierarchical label space. Experiments show that TELEClass can outperform previous weakly-supervised methods and LLM-based zero-shot prompting methods on two public datasets.

Entity set expansion, taxonomy expansion, and seed-guided taxonomy construction are three representative tasks that aim to automatically populate an existing taxonomy with new concepts. Previous studies view them as three separate tasks, and the proposed methods usually only work for one specific task, which lack generalizability and a holistic perspective across different tasks. In this paper, we aim to discover a unified solution to all three tasks. To be specific, we identify two common skills needed for entity set expansion, taxonomy expansion, and seed-guided taxonomy construction: finding "siblings" and finding "parents". We introduce a taxonomy-guided instruction tuning framework to teach a large language model to generate siblings and parents for query entities, where the joint pre-training process facilitates the mutual enhancement of these two skills. Extensive experiments on multiple benchmark datasets demonstrate the efficacy of our proposed TaxoInstruct framework, which outperforms task-specific baselines across all three tasks.

Accurately typing entity mentions from text segments is a fundamental task for various natural language processing applications. Many previous approaches rely on massive human-annotated data to perform entity typing. Nevertheless, collecting such data in highly specialized science and engineering domains (e.g., software engineering and security) can be time-consuming and costly, without mentioning the domain gaps between training and inference data if the model needs to be applied to confidential datasets. In this paper, we study the task of seed-guided fine-grained entity typing in science and engineering domains, which takes the name and a few seed entities for each entity type as the only supervision and aims to classify new entity mentions into both seen and unseen types (i.e., those without seed entities). To solve this problem, we propose SEType which first enriches the weak supervision by finding more entities for each seen type from an unlabeled corpus using the contextualized representations of pre-trained language models. It then matches the enriched entities to unlabeled text to get pseudo-labeled samples and trains a textual entailment model that can make inferences for both seen and unseen types. Extensive experiments on two datasets covering four domains demonstrate the effectiveness of SEType in comparison with various baselines., Comment: 9 pages; Accepted to AAAI 2024 (Code: https://github.com/yuzhimanhua/SEType)

Fine-grained entity typing (FET) is the task of identifying specific entity types at a fine-grained level for entity mentions based on their contextual information. Conventional methods for FET require extensive human annotation, which is time-consuming and costly. Recent studies have been developing weakly supervised or zero-shot approaches. We study the setting of zero-shot FET where only an ontology is provided. However, most existing ontology structures lack rich supporting information and even contain ambiguous relations, making them ineffective in guiding FET. Recently developed language models, though promising in various few-shot and zero-shot NLP tasks, may face challenges in zero-shot FET due to their lack of interaction with task-specific ontology. In this study, we propose OnEFET, where we (1) enrich each node in the ontology structure with two types of extra information: instance information for training sample augmentation and topic information to relate types to contexts, and (2) develop a coarse-to-fine typing algorithm that exploits the enriched information by training an entailment model with contrasting topics and instance-based augmented training samples. Our experiments show that OnEFET achieves high-quality fine-grained entity typing without human annotation, outperforming existing zero-shot methods by a large margin and rivaling supervised methods.

Independent or i.i.d. innovations is an essential assumption in the literature for analyzing a vector time series. However, this assumption is either too restrictive for a real-life time series to satisfy or is hard to verify through a hypothesis test. This paper performs statistical inference on a sparse high-dimensional vector autoregressive time series, allowing its white noise innovations to be dependent, even non-stationary. To achieve this goal, it adopts a post-selection estimator to fit the vector autoregressive model and derives the asymptotic distribution of the post-selection estimator. The innovations in the autoregressive time series are not assumed to be independent, thus making the covariance matrices of the autoregressive coefficient estimators complex and difficult to estimate. Our work develops a bootstrap algorithm to facilitate practitioners in performing statistical inference without having to engage in sophisticated calculations. Simulations and real-life data experiments reveal the validity of the proposed methods and theoretical results. Real-life data is rarely considered to exactly satisfy an autoregressive model with independent or i.i.d. innovations, so our work should better reflect the reality compared to the literature that assumes i.i.d. innovations., Comment: 62 pages, 5 figures, 4 tables

Instead of relying on human-annotated training samples to build a classifier, weakly supervised scientific paper classification aims to classify papers only using category descriptions (e.g., category names, category-indicative keywords). Existing studies on weakly supervised paper classification are less concerned with two challenges: (1) Papers should be classified into not only coarse-grained research topics but also fine-grained themes, and potentially into multiple themes, given a large and fine-grained label space; and (2) full text should be utilized to complement the paper title and abstract for classification. Moreover, instead of viewing the entire paper as a long linear sequence, one should exploit the structural information such as citation links across papers and the hierarchy of sections and paragraphs in each paper. To tackle these challenges, in this study, we propose FUTEX, a framework that uses the cross-paper network structure and the in-paper hierarchy structure to classify full-text scientific papers under weak supervision. A network-aware contrastive fine-tuning module and a hierarchy-aware aggregation module are designed to leverage the two types of structural signals, respectively. Experiments on two benchmark datasets demonstrate that FUTEX significantly outperforms competitive baselines and is on par with fully supervised classifiers that use 1,000 to 60,000 ground-truth training samples., Comment: 12 pages; Accepted to KDD 2023 (Code: https://github.com/yuzhimanhua/FUTEX)

Weakly-supervised text classification trains a classifier using the label name of each target class as the only supervision, which largely reduces human annotation efforts. Most existing methods first use the label names as static keyword-based features to generate pseudo labels, which are then used for final classifier training. While reasonable, such a commonly adopted framework suffers from two limitations: (1) keywords can have different meanings in different contexts and some text may not have any keyword, so keyword matching can induce noisy and inadequate pseudo labels; (2) the errors made in the pseudo label generation stage will directly propagate to the classifier training stage without a chance of being corrected. In this paper, we propose a new method, PIEClass, consisting of two modules: (1) a pseudo label acquisition module that uses zero-shot prompting of pre-trained language models (PLM) to get pseudo labels based on contextualized text understanding beyond static keyword matching, and (2) a noise-robust iterative ensemble training module that iteratively trains classifiers and updates pseudo labels by utilizing two PLM fine-tuning methods that regularize each other. Extensive experiments show that PIEClass achieves overall better performance than existing strong baselines on seven benchmark datasets and even achieves similar performance to fully-supervised classifiers on sentiment classification tasks., Comment: Accepted to EMNLP 2023 Main Conference

Unsupervised discovery of stories with correlated news articles in real-time helps people digest massive news streams without expensive human annotations. A common approach of the existing studies for unsupervised online story discovery is to represent news articles with symbolic- or graph-based embedding and incrementally cluster them into stories. Recent large language models are expected to improve the embedding further, but a straightforward adoption of the models by indiscriminately encoding all information in articles is ineffective to deal with text-rich and evolving news streams. In this work, we propose a novel thematic embedding with an off-the-shelf pretrained sentence encoder to dynamically represent articles and stories by considering their shared temporal themes. To realize the idea for unsupervised online story discovery, a scalable framework USTORY is introduced with two main techniques, theme- and time-aware dynamic embedding and novelty-aware adaptive clustering, fueled by lightweight story summaries. A thorough evaluation with real news data sets demonstrates that USTORY achieves higher story discovery performances than baselines while being robust and scalable to various streaming settings., Comment: Accepted by SIGIR'23

Instead of mining coherent topics from a given text corpus in a completely unsupervised manner, seed-guided topic discovery methods leverage user-provided seed words to extract distinctive and coherent topics so that the mined topics can better cater to the user's interest. To model the semantic correlation between words and seeds for discovering topic-indicative terms, existing seed-guided approaches utilize different types of context signals, such as document-level word co-occurrences, sliding window-based local contexts, and generic linguistic knowledge brought by pre-trained language models. In this work, we analyze and show empirically that each type of context information has its value and limitation in modeling word semantics under seed guidance, but combining three types of contexts (i.e., word embeddings learned from local contexts, pre-trained language model representations obtained from general-domain training, and topic-indicative sentences retrieved based on seed information) allows them to complement each other for discovering quality topics. We propose an iterative framework, SeedTopicMine, which jointly learns from the three types of contexts and gradually fuses their context signals via an ensemble ranking process. Under various sets of seeds and on multiple datasets, SeedTopicMine consistently yields more coherent and accurate topics than existing seed-guided topic discovery approaches., Comment: 9 pages; Accepted to WSDM 2023

Given a few seed entities of a certain type (e.g., Software or Programming Language), entity set expansion aims to discover an extensive set of entities that share the same type as the seeds. Entity set expansion in software-related domains such as StackOverflow can benefit many downstream tasks (e.g., software knowledge graph construction) and facilitate better IT operations and service management. Meanwhile, existing approaches are less concerned with two problems: (1) How to deal with multiple types of seed entities simultaneously? (2) How to leverage the power of pre-trained language models (PLMs)? Being aware of these two problems, in this paper, we study the entity set co-expansion task in StackOverflow, which extracts Library, OS, Application, and Language entities from StackOverflow question-answer threads. During the co-expansion process, we use PLMs to derive embeddings of candidate entities for calculating similarities between entities. Experimental results show that our proposed SECoExpan framework outperforms previous approaches significantly., Comment: 4 pages; Accepted to IEEE BigData 2022

Automated event detection from news corpora is a crucial task towards mining fast-evolving structured knowledge. As real-world events have different granularities, from the top-level themes to key events and then to event mentions corresponding to concrete actions, there are generally two lines of research: (1) theme detection identifies from a news corpus major themes (e.g., "2019 Hong Kong Protests" vs. "2020 U.S. Presidential Election") that have very distinct semantics; and (2) action extraction extracts from one document mention-level actions (e.g., "the police hit the left arm of the protester") that are too fine-grained for comprehending the event. In this paper, we propose a new task, key event detection at the intermediate level, aiming to detect from a news corpus key events (e.g., "HK Airport Protest on Aug. 12-14"), each happening at a particular time/location and focusing on the same topic. This task can bridge event understanding and structuring and is inherently challenging because of the thematic and temporal closeness of key events and the scarcity of labeled data due to the fast-evolving nature of news articles. To address these challenges, we develop an unsupervised key event detection framework, EvMine, that (1) extracts temporally frequent peak phrases using a novel ttf-itf score, (2) merges peak phrases into event-indicative feature sets by detecting communities from our designed peak phrase graph that captures document co-occurrences, semantic similarities, and temporal closeness signals, and (3) iteratively retrieves documents related to each key event by training a classifier with automatically generated pseudo labels from the event-indicative feature sets and refining the detected key events using the retrieved documents. Extensive experiments and case studies show EvMine outperforms all the baseline methods and its ablations on two real-world news corpora., Comment: Accepted to KDD 2022 Research Track

Topic models have been the prominent tools for automatic topic discovery from text corpora. Despite their effectiveness, topic models suffer from several limitations including the inability of modeling word ordering information in documents, the difficulty of incorporating external linguistic knowledge, and the lack of both accurate and efficient inference methods for approximating the intractable posterior. Recently, pretrained language models (PLMs) have brought astonishing performance improvements to a wide variety of tasks due to their superior representations of text. Interestingly, there have not been standard approaches to deploy PLMs for topic discovery as better alternatives to topic models. In this paper, we begin by analyzing the challenges of using PLM representations for topic discovery, and then propose a joint latent space learning and clustering framework built upon PLM embeddings. In the latent space, topic-word and document-topic distributions are jointly modeled so that the discovered topics can be interpreted by coherent and distinctive terms and meanwhile serve as meaningful summaries of the documents. Our model effectively leverages the strong representation power and superb linguistic features brought by PLMs for topic discovery, and is conceptually simpler than topic models. On two benchmark datasets in different domains, our model generates significantly more coherent and diverse topics than strong topic models, and offers better topic-wise document representations, based on both automatic and human evaluations., Comment: WWW 2022. (Code: https://github.com/yumeng5/TopClus)

Focusing on a high dimensional linear model $y = X\beta + \epsilon$ with dependent, non-stationary, and heteroskedastic errors, this paper applies the debiased and threshold ridge regression method that gives a consistent estimator for linear combinations of $\beta$; and derives a Gaussian approximation theorem for the estimator. Besides, it proposes a dependent wild bootstrap algorithm to construct the estimator's confidence intervals and perform hypothesis testing. Numerical experiments on the proposed estimator and the bootstrap algorithm show that they have favorable finite sample performance. Research on a high dimensional linear model with dependent(non-stationary) errors is sparse, and our work should bring some new insights to this field., Comment: 39 pages, 3 figures, 3 tables

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimation obtained by fitting a (linear) autoregressive model to a general weakly stationary time series is revisited and a Gaussian approximation theorem for the maximum of the estimators of the autoregressive coefficients is derived. To perform statistical inference for the second order parameters considered, a bootstrap algorithm, the so-called second-order wild bootstrap, is applied. Consistency of this bootstrap procedure is proven. In contrast to existing bootstrap alternatives, validity of the second-order wild bootstrap does not require the imposition of strict stationary conditions or structural process assumptions, like linearity. The good finite sample performance of the second-order wild bootstrap is demonstrated by means of simulations., Comment: 66 pages, 1 table, 2 figures

We study the problem of training named entity recognition (NER) models using only distantly-labeled data, which can be automatically obtained by matching entity mentions in the raw text with entity types in a knowledge base. The biggest challenge of distantly-supervised NER is that the distant supervision may induce incomplete and noisy labels, rendering the straightforward application of supervised learning ineffective. In this paper, we propose (1) a noise-robust learning scheme comprised of a new loss function and a noisy label removal step, for training NER models on distantly-labeled data, and (2) a self-training method that uses contextualized augmentations created by pre-trained language models to improve the generalization ability of the NER model. On three benchmark datasets, our method achieves superior performance, outperforming existing distantly-supervised NER models by significant margins., Comment: EMNLP 2021. (Code: https://github.com/yumeng5/RoSTER)

Traditional event extraction methods require predefined event types and their corresponding annotations to learn event extractors. These prerequisites are often hard to be satisfied in real-world applications. This work presents a corpus-based open-domain event type induction method that automatically discovers a set of event types from a given corpus. As events of the same type could be expressed in multiple ways, we propose to represent each event type as a cluster of pairs. Specifically, our method (1) selects salient predicates and object heads, (2) disambiguates predicate senses using only a verb sense dictionary, and (3) obtains event types by jointly embedding and clustering pairs in a latent spherical space. Our experiments, on three datasets from different domains, show our method can discover salient and high-quality event types, according to both automatic and human evaluations., Comment: 15 pages, EMNLP 2021 main conference, updated for new related work

Contrastive learning has been applied successfully to learn vector representations of text. Previous research demonstrated that learning high-quality representations benefits from batch-wise contrastive loss with a large number of negatives. In practice, the technique of in-batch negative is used, where for each example in a batch, other batch examples' positives will be taken as its negatives, avoiding encoding extra negatives. This, however, still conditions each example's loss on all batch examples and requires fitting the entire large batch into GPU memory. This paper introduces a gradient caching technique that decouples backpropagation between contrastive loss and the encoder, removing encoder backward pass data dependency along the batch dimension. As a result, gradients can be computed for one subset of the batch at a time, leading to almost constant memory usage., Comment: RepL4NLP 2021

Current text classification methods typically require a good number of human-labeled documents as training data, which can be costly and difficult to obtain in real applications. Humans can perform classification without seeing any labeled examples but only based on a small set of words describing the categories to be classified. In this paper, we explore the potential of only using the label name of each class to train classification models on unlabeled data, without using any labeled documents. We use pre-trained neural language models both as general linguistic knowledge sources for category understanding and as representation learning models for document classification. Our method (1) associates semantically related words with the label names, (2) finds category-indicative words and trains the model to predict their implied categories, and (3) generalizes the model via self-training. We show that our model achieves around 90% accuracy on four benchmark datasets including topic and sentiment classification without using any labeled documents but learning from unlabeled data supervised by at most 3 words (1 in most cases) per class as the label name., Comment: EMNLP 2020. (Code: https://github.com/yumeng5/LOTClass)

Taxonomy is not only a fundamental form of knowledge representation, but also crucial to vast knowledge-rich applications, such as question answering and web search. Most existing taxonomy construction methods extract hypernym-hyponym entity pairs to organize a "universal" taxonomy. However, these generic taxonomies cannot satisfy user's specific interest in certain areas and relations. Moreover, the nature of instance taxonomy treats each node as a single word, which has low semantic coverage. In this paper, we propose a method for seed-guided topical taxonomy construction, which takes a corpus and a seed taxonomy described by concept names as input, and constructs a more complete taxonomy based on user's interest, wherein each node is represented by a cluster of coherent terms. Our framework, CoRel, has two modules to fulfill this goal. A relation transferring module learns and transfers the user's interested relation along multiple paths to expand the seed taxonomy structure in width and depth. A concept learning module enriches the semantics of each concept node by jointly embedding the taxonomy and text. Comprehensive experiments conducted on real-world datasets show that Corel generates high-quality topical taxonomies and outperforms all the baselines significantly., Comment: KDD 2020 Research Track

The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, i.e., zeroing out regression coefficients that are not significant. By contrast, classical ridge regression can not reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the model selection. As a consequence, ridge regression may be worth another look since -- after debiasing and thresholding -- it may offer some advantages over the Lasso, e.g., it can be easily computed using a closed-form expression. % and it has similar performance to threshold Lasso. In this paper, we define a debiased and thresholded ridge regression method, and prove a consistency result and a Gaussian approximation theorem. We further introduce a wild bootstrap algorithm to construct confidence regions and perform hypothesis testing for a linear combination of parameters. In addition to estimation, we consider the problem of prediction, and present a novel, hybrid bootstrap algorithm tailored for prediction intervals. Extensive numerical simulations further show that the debiased and thresholded ridge regression has favorable finite sample performance and may be preferable in some settings., Comment: 2 figures, 37 pages

Mining a set of meaningful topics organized into a hierarchy is intuitively appealing since topic correlations are ubiquitous in massive text corpora. To account for potential hierarchical topic structures, hierarchical topic models generalize flat topic models by incorporating latent topic hierarchies into their generative modeling process. However, due to their purely unsupervised nature, the learned topic hierarchy often deviates from users' particular needs or interests. To guide the hierarchical topic discovery process with minimal user supervision, we propose a new task, Hierarchical Topic Mining, which takes a category tree described by category names only, and aims to mine a set of representative terms for each category from a text corpus to help a user comprehend his/her interested topics. We develop a novel joint tree and text embedding method along with a principled optimization procedure that allows simultaneous modeling of the category tree structure and the corpus generative process in the spherical space for effective category-representative term discovery. Our comprehensive experiments show that our model, named JoSH, mines a high-quality set of hierarchical topics with high efficiency and benefits weakly-supervised hierarchical text classification tasks., Comment: KDD 2020 Research Track. (Code: https://github.com/yumeng5/JoSH)

It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately 50% probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations., Comment: 27 pages and 2 figures

Entity set expansion, aiming at expanding a small seed entity set with new entities belonging to the same semantic class, is a critical task that benefits many downstream NLP and IR applications, such as question answering, query understanding, and taxonomy construction. Existing set expansion methods bootstrap the seed entity set by adaptively selecting context features and extracting new entities. A key challenge for entity set expansion is to avoid selecting ambiguous context features which will shift the class semantics and lead to accumulative errors in later iterations. In this study, we propose a novel iterative set expansion framework that leverages automatically generated class names to address the semantic drift issue. In each iteration, we select one positive and several negative class names by probing a pre-trained language model, and further score each candidate entity based on selected class names. Experiments on two datasets show that our framework generates high-quality class names and outperforms previous state-of-the-art methods significantly., Comment: ACL 2020

Given a small set of seed entities (e.g., ``USA'', ``Russia''), corpus-based set expansion is to induce an extensive set of entities which share the same semantic class (Country in this example) from a given corpus. Set expansion benefits a wide range of downstream applications in knowledge discovery, such as web search, taxonomy construction, and query suggestion. Existing corpus-based set expansion algorithms typically bootstrap the given seeds by incorporating lexical patterns and distributional similarity. However, due to no negative sets provided explicitly, these methods suffer from semantic drift caused by expanding the seed set freely without guidance. We propose a new framework, Set-CoExpan, that automatically generates auxiliary sets as negative sets that are closely related to the target set of user's interest, and then performs multiple sets co-expansion that extracts discriminative features by comparing target set with auxiliary sets, to form multiple cohesive sets that are distinctive from one another, thus resolving the semantic drift issue. In this paper we demonstrate that by generating auxiliary sets, we can guide the expansion process of target set to avoid touching those ambiguous areas around the border with auxiliary sets, and we show that Set-CoExpan outperforms strong baseline methods significantly., Comment: WWW 2020

Literatures in state space models focus on parametric inference and prediction, which fail if the state space model is not fully specified and the maximum likelihood estimation does not work. In this paper, we assume the state transition matrix and the distribution of state noises are unknown. Under this assumption, we provide methods to consistently estimate these terms. In addition, we introduce an algorithm to construct consistent prediction intervals for state vectors and future observations. We complement the asymptotic results with several numerical experiments., Comment: 22 pages, 1 figure

In this paper, we prove $L_p,\ p\geq 2$ and almost sure convergence of tail index estimator mentioned in \cite{grama2008} under random censoring and several assumptions. $p$th moment of the error of the estimator is proved to be of order $O\left(\frac{1}{\log^{m\kappa/2}n}\right)$ with given assumptions. We also perform several finite sample simulations to quantify performance of this estimator. Finite sample results show that the proposed estimator is effective in finding underlying tail index even when censor rate is high., Comment: There are totally 6 figures and 17 pages of this article

In this paper, the model $Y_i=g(Z_i),\ i=1,2,...,n$ with $Z_i$ being random variables with known distribution and $g(x)$ being unknown strictly increasing function is proposed and almost sure convergence of estimator for $g(x)$ is proved for i.i.d and short range dependent data. Confidence intervals and bands are constructed for i.i.d data theoretically and confidence intervals are introduced for short range dependent data through resampling. Besides, a test for equivalence of $g(x)$ to the desired function is proposed. Finite sample analysis and application of this model on an urban waste water treatment plant's data is demonstrated as well., Comment: 21 pages, 10 figures

Let $S_{a,b}$ denote the sequence of leading digits of $a^n$ in base $b$. It is well known that if $a$ is not a rational power of $b$, then the sequence $S_{a,b}$ satisfies Benford's Law; that is, digit $d$ occurs in $S_{a,b}$ with frequency $\log_{b}(1+1/d)$, for $d=1,2,\dots,b-1$. In this paper, we investigate the \emph{complexity} of such sequences. We focus mainly on the \emph{block complexity}, $p_{a,b}(n)$, defined as the number of distinct blocks of length $n$ appearing in $S_{a,b}$. In our main result we determine $p_{a,b}(n)$ for all squarefree bases $b\ge 5$ and all rational numbers $a>0$ that are not integral powers of $b$. In particular, we show that, for all such pairs $(a,b)$, the complexity function $p_{a,b}(n)$ is \emph{affine}, i.e., satisfies $p_{a,b}(n)=c_{a,b} n + d_{a,b}$ for all $n\ge1$, with coefficients $c_{a,b}\ge1$ and $d_{a,b}\ge0$, given explicitly in terms of $a$ and $b$. We also show that the requirement that $b$ be squarefree cannot be dropped: If $b$ is not squarefree, then there exist integers $a$ with $1