The Medium Access Control protocol of Power Line Communication networks (defined in Homeplug and IEEE 1901 standards) has received relatively modest attention from the research community. As a consequence, there is only one analytical model that complies with the standardised MAC procedures and considers unsaturated conditions. We identify two important limitations of the existing analytical model: high computational expense and predicted results just prior to the predicted saturation point do not correspond to long-term network performance. In this work, we present a simplification of the previously defined analytical model of Homeplug MAC able to substantially reduce its complexity and demonstrate that the previous performance results just before predicted saturation correspond to a transitory phase. We determine that the causes of previous misprediction are common analytical assumptions and the potential occurrence of a transitory phase, that we show to be of extremely long duration under certain circumstances. We also provide techniques, both analytical and experimental, to correctly predict long-term behaviour and analyse the effect of specific Homeplug IEEE 1901 features on the magnitude of misprediction errors. Our simplified analysis is then used to model the priority resolution scheme defined in Homeplug IEEE 1901. We show that previous tendencies found in simulations and in an off-the-shelf testbed are correctly captured in our framework. We also show that resorting to the traffic differentiation provided by the different contention parameters alone solves the starvation faced by lower-access category traffic.
Consequently, the analytic model in @cite_21 has been widely used both to derive performance metrics and as a basis for extension @cite_3 @cite_14 @cite_16 @cite_1 @cite_5 @cite_22 as it strictly follows the procedure defined in the standard and it considers saturated as well as unsaturated conditions. This widespread use motivates our improvements in terms of reducing complexity while maintaining the accuracy and retaining all features defined in the standard @cite_19 and understanding the transitory nature of the results predicted before saturation in @cite_21 .
@cite_14 @cite_22 @cite_21 @cite_1 @cite_3 @cite_19 @cite_5 @cite_16
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Abstract In this paper, we present a unifying analysis for redundancy systems with cancel-on-start ( c . o . s . ) and cancel-on-complete ( c . o . c . ) with exponentially distributed service requirements. With c . o . s . ( c . o . c . ) all redundant copies are removed as soon as one of the copies starts (completes) service. As a consequence, c . o . s . does not waste any computing resources, as opposed to c . o . c . We show that the c . o . s . model is equivalent to a queueing system with multi-type jobs and servers, which was analyzed in , (2012), and show that c . o . c . (under the assumption of i.i.d. copies) can be analyzed by a generalization of , (2012) where state-dependent departure rates are permitted. This allows us to show that the stationary distribution for both the c . o . c . and c . o . s . models has a product form. We give a detailed first-time analysis for c . o . s and derive a closed form expression for important metrics like mean number of jobs in the system, and probability of waiting. We also note that the c . o . s . model is equivalent to Join-Shortest-Work queue with power of d (JSW( d )). In the latter, an incoming job is dispatched to the server with smallest workload among d randomly chosen ones. Thus, all our results apply mutatis-mutandis to JSW( d ). Comparing the performance of c . o . s . with that of c . o . c . with i.i.d. copies gives the unexpected conclusion (since c . o . s . does not waste any resources) that c . o . s . is worse in terms of mean number of jobs. As part of ancillary results, we illustrate that this is primarily due to the assumption of i.i.d. copies in case of c . o . c . (together with exponentially distributed requirements) and that such assumptions might lead to conclusions that are qualitatively different from that observed in practice. Received 28 May 2002; revised 18 September 2002; accepted 24 September 2002; published 14 February 2003. [1] When an inverse problem is solved to estimate an unknown function such as the hydraulic conductivity in an aquifer or the contamination history at a site, one constraint is that the unknown function is known to be everywhere nonnegative. In this work, we develop a statistically rigorous method for enforcing function nonnegativity in Bayesian inverse problems. The proposed method behaves similarly to a Gaussian process with a linear variogram (i.e., unrestricted Brownian motion) for parameter values significantly greater than zero. The method uses the method of images to define a prior probability density function based on reflected Brownian motion that implicitly enforces nonnegativity. This work focuses on problems where the unknown is a function of a single variable (e.g., time). A Markov chain Monte Carlo (MCMC) method, specifically, a highly efficient Gibbs sampler, is implemented to generate conditional realizations of the unknown function. The new method is applied to the estimation of the trichloroethylene (TCE) and perchloroethylene (PCE) contamination history in an aquifer at Dover Air Force Base, Delaware, based on concentration profiles obtained from an underlying aquitard. INDEX TERMS: 1831 Hydrology: Groundwater quality; 1869 Hydrology: Stochastic processes; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: stochastic inverse modeling, contaminant source identification, inference under constraints, Markov chain Monte Carlo (MCMC), Gibbs sampling, Bayesian inference We consider MapReduce workloads that are produced by analytics applications. In contrast to ad hoc query workloads, analytics applications are comprised of fixed data flows that are run over newly arriving data sets or on different portions of an existing data set. Examples of such workloads include document analysis indexing, social media analytics, and ETL (Extract Transform Load). Motivated by these workloads, we propose a technique that predicts the runtime performance for a fixed set of queries running over varying input data sets. Our prediction technique splits each query into several segments where each segment’s performance is estimated using machine learning models. These per-segment estimates are plugged into a global analytical model to predict the overall query runtime. Our approach uses minimal statistics about the input data sets (e.g., tuple size, cardinality), which are complemented with historical information about prior query executions (e.g., execution time). We analyze the accuracy of predictions for several segment granularities on both standard analytical benchmarks such as TPC-DS [17], and on several real workloads. We obtain less than 25 prediction errors for 90 of predictions. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. We consider the problem of using a large unlabeled sample to boost performance of a learning algorit,hrn when only a small set of labeled examples is available. In particular, we consider a problem setting motivated by the task of learning to classify web pages, in which the description of each example can be partitioned into two distinct views. For example, the description of a web page can be partitioned into the words occurring on that page, and the words occurring in hyperlinks t,hat point to that page. We assume that either view of the example would be sufficient for learning if we had enough labeled data, but our goal is to use both views together to allow inexpensive unlabeled data to augment, a much smaller set of labeled examples. Specifically, the presence of two distinct views of each example suggests strategies in which two learning algorithms are trained separately on each view, and then each algorithm’s predictions on new unlabeled examples are used to enlarge the training set of the other. Our goal in this paper is to provide a PAC-style analysis for this setting, and, more broadly, a PAC-style framework for the general problem of learning from both labeled and unlabeled data. We also provide empirical results on real web-page data indicating that this use of unlabeled examples can lead to significant improvement of hypotheses in practice. *This research was supported in part by the DARPA HPKB program under contract F30602-97-1-0215 and by NSF National Young investigator grant CCR-9357793. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. TO copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or a fee. COLT 98 Madison WI USA Copyright ACM 1998 l-58113-057--0 98 7... 5.00 92 Tom Mitchell School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 mitchell+@cs.cmu.edu This paper presents a new approach for automatically deriving worst-case resource bounds for C programs. The described technique combines ideas from amortized analysis and abstract interpretation in a unified framework to address four challenges for state-of-the-art techniques: compositionality, user interaction, generation of proof certificates, and scalability. Compositionality is achieved by incorporating the potential method of amortized analysis. It enables the derivation of global whole-program bounds with local derivation rules by naturally tracking size changes of variables in sequenced loops and function calls. The resource consumption of functions is described abstractly and a function call can be analyzed without access to the function body. User interaction is supported with a new mechanism that clearly separates qualitative and quantitative verification. A user can guide the analysis to derive complex non-linear bounds by using auxiliary variables and assertions. The assertions are separately proved using established qualitative techniques such as abstract interpretation or Hoare logic. Proof certificates are automatically generated from the local derivation rules. A soundness proof of the derivation system with respect to a formal cost semantics guarantees the validity of the certificates. Scalability is attained by an efficient reduction of bound inference to a linear optimization problem that can be solved by off-the-shelf LP solvers. The analysis framework is implemented in the publicly-available tool C4B. An experimental evaluation demonstrates the advantages of the new technique with a comparison of C4B with existing tools on challenging micro benchmarks and the analysis of more than 2900 lines of C code from the cBench benchmark suite. Model checking and counter-example guided abstraction refinement are examples of applications of SAT solving requiring the production of models for satisfiable formulas. Better than giving a truth value to every variable, one can provide an implicant, i.e. a partial assignment of the variables such that every full extension is a model for the formula. An implicant is prime if every assignment is necessary. Since prime implicants contain no literal irrelevant for the satisfiability of the formula, they are considered as highly refined information. We here propose a novel algorithm that uses data structures found in modern CDCL SAT solvers to efficiently compute prime implicants starting from an existing model. The original aspects are (1) the algorithm is based on watched literals and a form of propagation of required literals, adapted to CDCL solvers (2) the algorithm works not only on clauses, but also on generalized constraints (3) for clauses and, more generally for cardinality constraints, the algorithm complexity is linear in the size of the constraints found. We implemented and evaluated the algorithm with the Sat4j library. As machine learning (ML) applications become increasingly prevalent, protecting the confidentiality of ML models becomes paramount for two reasons: (a) models may constitute a business advantage to its owner, and (b) an adversary may use a stolen model to find transferable adversarial examples that can be used to evade classification by the original model. One way to protect model confidentiality is to limit access to the model only via well-defined prediction APIs. This is common not only in machine-learning-as-a-service (MLaaS) settings where the model is remote, but also in scenarios like autonomous driving where the model is local but direct access to it is protected, for example, by hardware security mechanisms. Nevertheless, prediction APIs still leak information so that it is possible to mount model extraction attacks by an adversary who repeatedly queries the model via the prediction API. In this paper, we describe a new model extraction attack by combining a novel approach for generating synthetic queries together with recent advances in training deep neural networks. This attack outperforms state-of-the-art model extraction techniques in terms of transferability of targeted adversarial examples generated using the extracted model (+15-30 percentage points, pp), and in prediction accuracy (+15-20 pp) on two datasets. We then propose the first generic approach to effectively detect model extraction attacks: PRADA. It analyzes how the distribution of consecutive queries to the model evolves over time and raises an alarm when there are abrupt deviations. We show that PRADA can detect all known model extraction attacks with a 100 success rate and no false positives. PRADA is particularly suited for detecting extraction attacks against local models. Abstractive summarization aims to generate a shorter version of the document covering all the salient points in a compact and coherent fashion. On the other hand, query-based summarization highlights those points that are relevant in the context of a given query. The encode-attend-decode paradigm has achieved notable success in machine translation, extractive summarization, dialog systems, etc. But it suffers from the drawback of generation of repeated phrases. In this work we propose a model for the query-based summarization task based on the encode-attend-decode paradigm with two key additions (i) a query attention model (in addition to document attention model) which learns to focus on different portions of the query at different time steps (instead of using a static representation for the query) and (ii) a new diversity based attention model which aims to alleviate the problem of repeating phrases in the summary. In order to enable the testing of this model we introduce a new query-based summarization dataset building on debatepedia. Our experiments show that with these two additions the proposed model clearly outperforms vanilla encode-attend-decode models with a gain of 28 (absolute) in ROUGE-L scores. This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An e approximate quantile sketch receives a stream of items x1,·,xn and allows one to approximate the rank of any query item up to additive error e n with probability at least 1-δ.The rank of a query x is the number of stream items such that xi ≤ x. The minimal sketch size required for this task is trivially at least 1 e.Felber and Ostrovsky obtain a O((1 e)log(1 e)) space sketch for a fixed δ.Without restrictions on the nature of the stream or the ratio between e and n, no better upper or lower bounds were known to date. This paper obtains an O((1 e)log log (1 δ)) space sketch and a matching lower bound. This resolves the open problem and proves a qualitative gap between randomized and deterministic quantile sketching for which an Ω((1 e)log(1 e)) lower bound is known. One of our contributions is a novel representation and modification of the widely used merge-and-reduce construction. This modification allows for an analysis which is both tight and extremely simple. The same technique was reported, in private communications, to be useful for improving other sketching objectives and geometric coreset constructions. We address the verification problem of finite-state concurrent programs running under weak memory models. These models capture the reordering of program (read and write) operations done by modern multi-processor architectures for performance. The verification problem we study is crucial for the correctness of concurrency libraries and other performance-critical system services employing lock-free synchronization, as well as for the correctness of compiler backends that generate code targeted to run on such architectures. We consider in this paper combinations of three well-known program order relaxations. We consider first the "write to read" relaxation, which corresponds to the TSO (Total Store Ordering) model. This relaxation is used in most hardware architectures available today. Then, we consider models obtained by adding either (1) the "write to write" relaxation, leading to a model which is essentially PSO (Partial Store Ordering), or (2) the "read to read write" relaxation, or (3) both of them, as it is done in the RMO (Relaxed Memory Ordering) model for instance. We define abstract operational models for these weak memory models based on state machines with (potentially unbounded) FIFO buffers, and we investigate the decidability of their reachability and their repeated reachability problems. We prove that the reachability problem is decidable for the TSO model, as well as for its extension with "write to write" relaxation (PSO). Furthermore, we prove that the reachability problem becomes undecidable when the "read to read write" relaxation is added to either of these two memory models, and we give a condition under which this addition preserves the decidability of the reachability problem. We show also that the repeated reachability problem is undecidable for all the considered memory models. We learn a joint model of sentence extraction and compression for multi-document summarization. Our model scores candidate summaries according to a combined linear model whose features factor over (1) the n-gram types in the summary and (2) the compressions used. We train the model using a margin-based objective whose loss captures end summary quality. Because of the exponentially large set of candidate summaries, we use a cutting-plane algorithm to incrementally detect and add active constraints efficiently. Inference in our model can be cast as an ILP and thereby solved in reasonable time; we also present a fast approximation scheme which achieves similar performance. Our jointly extracted and compressed summaries outperform both unlearned baselines and our learned extraction-only system on both ROUGE and Pyramid, without a drop in judged linguistic quality. We achieve the highest published ROUGE results to date on the TAC 2008 data set. Reasoning about the performance of models of software systems typically entails the derivation of metrics such as throughput, utilization, and response time. If the model is a Markov chain, these are expressed as real functions of the chain, called reward models. The computational complexity of reward-based metrics is of the same order as the solution of the Markov chain, making the analysis infeasible when evaluating large-scale systems. In the context of the stochastic process algebra PEPA, the underlying continuous-time Markov chain has been shown to admit a deterministic (fluid) approximation as a solution of an ordinary differential equation, which effectively circumvents state-space explosion. This paper is concerned with approximating Markovian reward models for PEPA with fluid rewards, i.e., functions of the solution of the differential equation problem. It shows that (1) the Markovian reward models for typical metrics of performance enjoy asymptotic convergence to their fluid analogues, and that (2) via numerical tests, the approximation yields satisfactory accuracy in practice. In this paper, we present the results of long-term research conducted in order to study the contribution made by software models based on the Unified Modeling Language (UML) to the comprehensibility of Java source-code deprived of comments. We have conducted 12 controlled experiments in different experimental contexts and on different sites with participants with different levels of expertise (i.e., Bachelor’s, Master’s, and PhD students and software practitioners from Italy and Spain). A total of 333 observations were obtained from these experiments. The UML models in our experiments were those produced in the analysis and design phases. The models produced in the analysis phase were created with the objective of abstracting the environment in which the software will work (i.e., the problem domain), while those produced in the design phase were created with the goal of abstracting implementation aspects of the software (i.e., the solution application domain). Source-code comprehensibility was assessed with regard to correctness of understanding, time taken to accomplish the comprehension tasks, and efficiency as regards accomplishing those tasks. In order to study the global effect of UML models on source-code comprehensibility, we aggregated results from the individual experiments using a meta-analysis. We made every effort to account for the heterogeneity of our experiments when aggregating the results obtained from them. The overall results suggest that the use of UML models affects the comprehensibility of source-code, when it is deprived of comments. Indeed, models produced in the analysis phase might reduce source-code comprehensibility, while increasing the time taken to complete comprehension tasks. That is, browsing source code and this kind of models together negatively impacts on the time taken to complete comprehension tasks without having a positive effect on the comprehensibility of source code. One plausible justification for this is that the UML models produced in the analysis phase focus on the problem domain. That is, models produced in the analysis phase say nothing about source code and there should be no expectation that they would, in any way, be beneficial to comprehensibility. On the other hand, UML models produced in the design phase improve source-code comprehensibility. One possible justification for this result is that models produced in the design phase are more focused on implementation details. Therefore, although the participants had more material to read and browse, this additional effort was paid back in the form of an improved comprehension of source code. In this paper we present a novel framework for extracting the ratable aspects of objects from online user reviews. Extracting such aspects is an important challenge in automatically mining product opinions from the web and in generating opinion-based summaries of user reviews [18, 19, 7, 12, 27, 36, 21]. Our models are based on extensions to standard topic modeling methods such as LDA and PLSA to induce multi-grain topics. We argue that multi-grain models are more appropriate for our task since standard models tend to produce topics that correspond to global properties of objects (e.g., the brand of a product type) rather than the aspects of an object that tend to be rated by a user. The models we present not only extract ratable aspects, but also cluster them into coherent topics, e.g., 'waitress' and 'bartender' are part of the same topic 'staff' for restaurants. This differentiates it from much of the previous work which extracts aspects through term frequency analysis with minimal clustering. We evaluate the multi-grain models both qualitatively and quantitatively to show that they improve significantly upon standard topic models. In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10 –20 selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates. The clinical notes in a given patient record contain much redundancy, in large part due to clinicians’ documentation habit of copying from previous notes in the record and pasting into a new note. Previous work has shown that this redundancy has a negative impact on the quality of text mining and topic modeling in particular. In this paper we describe a novel variant of Latent Dirichlet Allocation (LDA) topic modeling, Red-LDA, which takes into account the inherent redundancy of patient records when modeling content of clinical notes. To assess the value of Red-LDA, we experiment with three baselines and our novel redundancy-aware topic modeling method: given a large collection of patient records, (i) apply vanilla LDA to all documents in all input records; (ii) identify and remove all redundancy by chosing a single representative document for each record as input to LDA; (iii) identify and remove all redundant paragraphs in each record, leaving partial, non-redundant documents as input to LDA; and (iv) apply Red-LDA to all documents in all input records. Both quantitative evaluation carried out through log-likelihood on held-out data and topic coherence of produced topics and qualitative assessement of topics carried out by physicians show that Red-LDA produces superior models to all three baseline strategies. This research contributes to the emerging field of understanding the characteristics of the electronic health record and how to account for them in the framework of data mining. The code for the two redundancy-elimination baselines and Red-LDA is made publicly available to the community. of the number of bits required to write down the observed data, has been reformulated to extend the classical maximum likelihood principle. The principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models; i.e., of the model structures. The principle rests on a new way to interpret and construct a universal prior distribution for the integers, which makes sense even when the parameter is an individual object. Truncated realvalued parameters are converted to integers by dividing them by their precision, and their prior is determined from the universal prior for the integers by optimizing the precision. 1. Introduction. In this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data, when each observation is given with some precision. Instead of attempting at an absolutely shortest description, which would be futile, we look for the optimum relative to a class of parametrically given distributions. This Minimum Description Length (MDL) principle, which we introduced in a less comprehensive form in [25], turns out to degenerate to the more familiar Maximum Likelihood (ML) principle in case the number of parameters in the models is fixed, so that the description length of the parameters themselves can be ignored. In another extreme case, where the parameters determine the data, it similarly degenerates to Jaynes's principle of maximum entropy, [14]. But the main power of the new criterion is that it permits estimates of the entire model, its parameters, their number, and even the way the parameters appear in the model; i.e., the model structure. Hence, there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or, perhaps, over parameterized. This paper deals with content-based large-scale image retrieval using the state-of-the-art framework of VLAD and Product Quantization proposed by Jegou as a starting point. Demonstrating an excellent accuracy-efficiency trade-off, this framework has attracted increased attention from the community and numerous extensions have been proposed. In this work, we make an in-depth analysis of the framework that aims at increasing our understanding of its different processing steps and boosting its overall performance. Our analysis involves the evaluation of numerous extensions (both existing and novel) as well as the study of the effects of several unexplored parameters. We specifically focus on: a) employing more efficient and discriminative local features; b) improving the quality of the aggregated representation; and c) optimizing the indexing scheme. Our thorough experimental evaluation provides new insights into extensions that consistently contribute, and others that do not, to performance improvement, and sheds light onto the effects of previously unexplored parameters of the framework. As a result, we develop an enhanced framework that significantly outperforms the previous best reported accuracy results on standard benchmarks and is more efficient. This paper addresses the independent assumption issue in classifier fusion process. In the last decade, dependency modeling techniques were developed under some specific assumptions which may not be valid in practical applications. In this paper, using analytical functions on posterior probabilities of each feature, we propose a new framework to model dependency without those assumptions. With the analytical dependency model (ADM), we give an equivalent condition to the independent assumption from the properties of marginal distributions, and show that the proposed ADM can model dependency. Since ADM may contain infinite number of undetermined coefficients, we further propose a reduced form of ADM, based on the convergent properties of analytical functions. Finally, under the regularized least square criterion, an optimal Reduced Analytical Dependency Model (RADM) is learned by approximating posterior probabilities such that all training samples are correctly classified. Experimental results show that the proposed RADM outperforms existing classifier fusion methods on Digit, Flower, Face and Human Action databases.