Dealing with sparse, long-tailed datasets, and cold-start problems is always a challenge for recommender systems. These issues can partly be dealt with by making predictions not in isolation, but by leveraging information from related events; such information could include signals from social relationships or from the sequence of recent activities. Both types of additional information can be used to improve the performance of state-of-the-art matrix factorization-based techniques. In this paper, we propose new methods to combine both social and sequential information simultaneously, in order to further improve recommendation performance. We show these techniques to be particularly effective when dealing with sparsity and cold-start issues in several large, real-world datasets.
Sequential recommendation. Markov chains are powerful methods for modeling stochastic transitions; they have been leveraged to model decision processes (e.g. @cite_16 ) and more generally uncover sequential patterns (e.g. @cite_21 @cite_10 ). In the sequential recommendation domain, Rendle proposed FPMC that combines MF and (factorized) Markov chains to be able to capture personalization and sequential patterns simultaneously @cite_15 . Our work follows this thread but extends these ideas by making use of social, in addition to sequential, dynamics.
@cite_15 @cite_16 @cite_10 @cite_21
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Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned - thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization. Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long- and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations. Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long-and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations. Markov chain Monte Carlo (MCMC) methods have been used in many fields (physics, chemistry, biology, and computer science) for simulation, inference, and optimization. In many applications, Markov chains are simulated for sampling from target probabilities π(X) defined on graphs G. The graph vertices represent elements of the system, the edges represent spatial relationships, while X is a vector of variables on the vertices which often take discrete values called labels or colors. Designing efficient Markov chains is a challenging task when the variables are strongly coupled. Because of this, methods such as the single-site Gibbs sampler often experience suboptimal performance. A well-celebrated algorithm, the Swendsen–Wang (SW) method, can address the coupling problem. It clusters the vertices as connected components after turning off some edges probabilistically, and changes the color of one cluster as a whole. It is known to mix rapidly under certain conditions. Unfortunately, the SW method has limited ... Spatial and temporal contextual information plays a key role for analyzing user behaviors, and is helpful for predicting where he or she will go next. With the growing ability of collecting information, more and more temporal and spatial contextual information is collected in systems, and the location prediction problem becomes crucial and feasible. Some works have been proposed to address this problem, but they all have their limitations. Factorizing Personalized Markov Chain (FPMC) is constructed based on a strong independence assumption among different factors, which limits its performance. Tensor Factorization (TF) faces the cold start problem in predicting future actions. Recurrent Neural Networks (RNN) model shows promising performance comparing with PFMC and TF, but all these methods have problem in modeling continuous time interval and geographical distance. In this paper, we extend RNN and propose a novel method called Spatial Temporal Recurrent Neural Networks (ST-RNN). ST-RNN can model local temporal and spatial contexts in each layer with time-specific transition matrices for different time intervals and distance-specific transition matrices for different geographical distances. Experimental results show that the proposed ST-RNN model yields significant improvements over the competitive compared methods on two typical datasets, i.e., Global Terrorism Database (GTD) and Gowalla dataset. This paper analyzes the optimum constant contention window (CW) for the HomePlug 1.0 and AV CSMA CA MAC. A discrete time, homogenous Markov chain, with the state specified by both the backoff counter (BC) and deferral counter (DC), is used to model a single node contending for transmission. The structure of the Markov chain admits a generalized expression for the stationary state probability mass function (pmf) associated with each state. The recursively defined state pmfs can be analytically reduced to a single expression relating the probability p, of the node finding the medium idle, the maximum window size W, the maximum deferral counter size, and the number of nodes n. Optimizing the MAC efficiency provides a target value for p, which can be attained with the proper selection of W and. It is shown that an optimal contention window size can be chosen based on a linear relationship with the number of nodes. Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings under the target densities or big scale differences. In this study, we propose a novel SG-MCMC method that takes the local geometry into account by using ideas from Quasi-Newton optimization methods. These second order methods directly approximate the inverse Hessian by using a limited history of samples and their gradients. Our method uses dense approximations of the inverse Hessian while keeping the time and memory complexities linear with the dimension of the problem. We provide a formal theoretical analysis where we show that the proposed method is asymptotically unbiased and consistent with the posterior expectations. We illustrate the effectiveness of the approach on both synthetic and real datasets. Our experiments on two challenging applications show that our method achieves fast convergence rates similar to Riemannian approaches while at the same time having low computational requirements similar to diagonal preconditioning approaches. Sequential recommendation is a fundamental task for network applications, and it usually suffers from the item cold start problem due to the insufficiency of user feedbacks. There are currently three kinds of popular approaches which are respectively based on matrix factorization (MF) of collaborative filtering, Markov chain (MC), and recurrent neural network (RNN). Although widely used, they have some limitations. MF based methods could not capture dynamic user's interest. The strong Markov assumption greatly limits the performance of MC based methods. RNN based methods are still in the early stage of incorporating additional information. Based on these basic models, many methods with additional information only validate incorporating one modality in a separate way. In this work, to make the sequential recommendation and deal with the item cold start problem, we propose a Multi-View Recurrent Neural Network (MV-RNN ) model. Given the latent feature, MV-RNN can alleviate the item cold start problem by incorporating visual and textual information. First, At the input of MV-RNN, three different combinations of multi-view features are studied, like concatenation, fusion by addition and fusion by reconstructing the original multi-modal data. MV-RNN applies the recurrent structure to dynamically capture the user's interest. Second, we design a separate structure and a united structure on the hidden state of MV-RNN to explore a more effective way to handle multi-view features. Experiments on two real-world datasets show that MV-RNN can effectively generate the personalized ranking list, tackle the missing modalities problem and significantly alleviate the item cold start problem. Top-N sequential recommendation models each user as a sequence of items interacted in the past and aims to predict top-N ranked items that a user will likely interact in a »near future». The order of interaction implies that sequential patterns play an important role where more recent items in a sequence have a larger impact on the next item. In this paper, we propose a Convolutional Sequence Embedding Recommendation Model »Caser» as a solution to address this requirement. The idea is to embed a sequence of recent items into an »image» in the time and latent spaces and learn sequential patterns as local features of the image using convolutional filters. This approach provides a unified and flexible network structure for capturing both general preferences and sequential patterns. The experiments on public data sets demonstrated that Caser consistently outperforms state-of-the-art sequential recommendation methods on a variety of common evaluation metrics. The Markov Chain Monte Carlo (MCMC) family of methods form a valuable part of the toolbox of social modeling and prediction techniques, enabling modelers to generate samples and summary statistics of a population of interest with minimal information. It has been used successfully to model changes over time in many types of social systems, including patterns of disease spread, adolescent smoking, and geopolitical conflicts. In MCMC an initial proposal distribution is iteratively refined until it approximates the posterior distribution. However, the selection of the proposal distribution can have a significant impact on model convergence. In this paper, we propose a new hybrid modeling technique in which an agent-based model is used to initialize the proposal distribution of the MCMC simulation. We demonstrate the use of our modeling technique in an urban transportation prediction scenario and show that the hybrid combined model produces more accurate predictions than either of the parent models. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. We propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models. Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SGMCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key components: i) adaptive preconditioners (as in ADAgrad or RMSprop), and ii) adaptive element-wise momentum weights. The zerotemperature limit gives a novel stochastic optimization method with adaptive elementwise momentum weights, while conventional optimization methods only have a shared, static momentum weight. Under certain assumptions, our theoretical analysis suggests the proposed simulated annealing approach converges close to the global optima. Experiments on several deep neural network models show state-of-the-art results compared to related stochastic optimization algorithms. This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a three-valued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique. Next basket recommendation becomes an increasing concern. Most conventional models explore either sequential transaction features or general interests of users. Further, some works treat users' general interests and sequential behaviors as two totally divided matters, and then combine them in some way for next basket recommendation. Moreover, the state-of-the-art models are based on the assumption of Markov Chains (MC), which only capture local sequential features between two adjacent baskets. In this work, we propose a novel model, Dynamic REcurrent bAsket Model (DREAM), based on Recurrent Neural Network (RNN). DREAM not only learns a dynamic representation of a user but also captures global sequential features among baskets. The dynamic representation of a specific user can reveal user's dynamic interests at different time, and the global sequential features reflect interactions of all baskets of the user over time. Experiment results on two public datasets indicate that DREAM is more effective than the state-of-the-art models for next basket recommendation. Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results. Personalized point-of-interest (POI) recommendation is a significant task in location-based social networks (LBSNs) as it can help provide better user experience as well as enable third-party services, e.g., launching advertisements. To provide a good recommendation, various research has been conducted in the literature. However, pervious efforts mainly consider the "check-ins" in a whole and omit their temporal relation. They can only recommend POI globally and cannot know where a user would like to go tomorrow or in the next few days. In this paper, we consider the task of successive personalized POI recommendation in LBSNs, which is a much harder task than standard personalized POI recommendation or prediction. To solve this task, we observe two prominent properties in the check-in sequence: personalized Markov chain and region localization. Hence, we propose a novel matrix factorization method, namely FPMC-LR, to embed the personalized Markov chains and the localized regions. Our proposed FPMC-LR not only exploits the personalized Markov chain in the check-in sequence, but also takes into account users' movement constraint, i.e., moving around a localized region. More importantly, utilizing the information of localized regions, we not only reduce the computation cost largely, but also discard the noisy information to boost recommendation. Results on two real-world LBSNs datasets demonstrate the merits of our proposed FPMC-LR. Markov chains with Labelled Transitions can be used to generate test cases in a model-based approach. These test cases are generated by random walks on the model according to probabilities associated with transitions. When these probabilities correspond to a usage profile, reliability may be estimated. However, in early stages of development, such probabilities are not easy to determine, thus default profiles must be considered. In such a case it may be interesting to target some coverage criteria rather to use classical uniform probability generation approach. In this paper we enrich an existing industrial tool based on usage profile with 3 possibilities to create default profiles that improve transition coverage. We report experiments that compare the improvement of the coverage rates by our approaches with respect to uniform probabilities on transitions from a given state, which is the current default profile. We present a method for controlling the output of procedural modeling programs using Sequential Monte Carlo (SMC). Previous probabilistic methods for controlling procedural models use Markov Chain Monte Carlo (MCMC), which receives control feedback only for completely-generated models. In contrast, SMC receives feedback incrementally on incomplete models, allowing it to reallocate computational resources and converge quickly. To handle the many possible sequentializations of a structured, recursive procedural modeling program, we develop and prove the correctness of a new SMC variant, Stochastically-Ordered Sequential Monte Carlo (SOSMC). We implement SOSMC for general-purpose programs using a new programming primitive: the stochastic future. Finally, we show that SOSMC reliably generates high-quality outputs for a variety of programs and control scoring functions. For small computational budgets, SOSMC's outputs often score nearly twice as high as those of MCMC or normal SMC. Point-of-interest (POI) recommendation is an important application for location-based social networks (LBSNs), which learns the user preference and mobility pattern from check-in sequences to recommend POIs. Previous studies show that modeling the sequential pattern of user check-ins is necessary for POI recommendation. Markov chain model, recurrent neural network, and the word2vec framework are used to model check-in sequences in previous work. However, all previous sequential models ignore the fact that check-in sequences on different days naturally exhibit the various temporal characteristics, for instance, "work" on weekday and "entertainment" on weekend. In this paper, we take this challenge and propose a Geo-Temporal sequential embedding rank (Geo-Teaser) model for POI recommendation. Inspired by the success of the word2vec framework to model the sequential contexts, we propose a temporal POI embedding model to learn POI representations under some particular temporal state. The temporal POI embedding model captures the contextual check-in information in sequences and the various temporal characteristics on different days as well. Furthermore, We propose a new way to incorporate the geographical influence into the pairwise preference ranking method through discriminating the unvisited POIs according to geographical information. Then we develop a geographically hierarchical pairwise preference ranking model. Finally, we propose a unified framework to recommend POIs combining these two models. To verify the effectiveness of our proposed method, we conduct experiments on two real-life datasets. Experimental results show that the Geo-Teaser model outperforms state-of-the-art models. Compared with the best baseline competitor, the Geo-Teaser model improves at least 20 on both datasets for all metrics. Abstract Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models computationally tractable, they rely on a number of assumptions that—as is well known—may not be realistic for the domain of application; in particular, the ability to provide exact numerical parameter assessments, and the applicability of time-homogeneity and the eponymous Markov property. In this work, we extend these models to imprecise continuous-time Markov chains (ICTMC's), which are a robust generalisation that relaxes these assumptions while remaining computationally tractable. More technically, an ICTMC is a set of “precise” continuous-time finite-state stochastic processes, and rather than computing expected values of functions, we seek to compute lower expectations , which are tight lower bounds on the expectations that correspond to such a set of “precise” models. Note that, in contrast to e.g. Bayesian methods, all the elements of such a set are treated on equal grounds; we do not consider a distribution over this set. Together with the conjugate notion of upper expectation , the bounds that we provide can then be intuitively interpreted as providing best- and worst-case scenarios with respect to all the models in our set of stochastic processes. The first part of this paper develops a formalism for describing continuous-time finite-state stochastic processes that does not require the aforementioned simplifying assumptions. Next, this formalism is used to characterise ICTMC's and to investigate their properties. The concept of lower expectation is then given an alternative operator-theoretic characterisation, by means of a lower transition operator , and the properties of this operator are investigated as well. Finally, we use this lower transition operator to derive tractable algorithms (with polynomial runtime complexity w.r.t. the maximum numerical error) for computing the lower expectation of functions that depend on the state at any finite number of time points.