OTFusion, or layer-wise model fusion via optimal transport, applies soft neuron association to unify different pre-trained networks. Despite its effectiveness in saving computational resources, OTFusion requires the input networks to have the same number of layers. To address this issue, we propose a novel model fusion framework, named CLAFusion, to fuse neural networks with different numbers of layers, which we refer to as heterogeneous neural networks, via cross-layer alignment. We demonstrate that the cross-layer alignment problem, which is an unbalanced assignment problem, can be solved efficiently using dynamic programming. Based on the cross-layer alignment, our framework balances the number of layers of neural networks before applying layer-wise model fusion. Our experiments indicate that CLAFusion, with an extra finetuning process, improves the accuracy of residual networks on the CIFAR10, CIFAR100, and Tiny-ImageNet datasets. Furthermore, we explore its practical usage for model compression and knowledge distillation when applied to the teacher-student setting.

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out experiments on various applications including deep generative models, deep domain adaptation, approximate Bayesian computation, color transfer, and gradient flow to show that the BoMb-OT can be widely applied and performs well in various applications.

Deep domain adaptation (DDA) approaches have recently been shown to perform better than their shallow rivals with better modeling capacity on complex domains (e.g., image, structural data, and sequential data). The underlying idea is to learn domain invariant representations on a latent space that can bridge the gap between source and target domains. Several theoretical studies have established insightful understanding and the benefit of learning domain invariant features; however, they are usually limited to the case where there is no label shift, hence hindering its applicability. In this paper, we propose and study a new challenging setting that allows us to use a Wasserstein distance (WS) to not only quantify the data shift but also to define the label shift directly. We further develop a theory to demonstrate that minimizing the WS of the data shift leads to closing the gap between the source and target data distributions on the latent space (e.g., an intermediate layer of a deep net), while still being able to quantify the label shift with respect to this latent space. Interestingly, our theory can consequently explain certain drawbacks of learning domain invariant features on the latent space. Finally, grounded on the results and guidance of our developed theory, we propose the Label Matching Deep Domain Adaptation (LAMDA) approach that outperforms baselines on real-world datasets for DA problems.

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost of robust optimal transport in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, in which $n$ is the number of supports of the probability distributions and $\varepsilon$ is the desired error. Furthermore, we investigate a fixed-support robust barycenter problem between $m$ discrete probability distributions with at most $n$ number of supports and develop an approximating algorithm based on iterative Bregman projections (IBP). For the specific case $m = 2$, we show that this algorithm can approximate the optimal barycenter value in $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon})$ time, thus being better than the previous complexity $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon^2})$ of the IBP algorithm for approximating the Wasserstein barycenter.

Domain adaptation (DA) benefits from the rigorous theoretical works that study its insightful characteristics and various aspects, e.g., learning domain-invariant representations and its trade-off. However, it seems not the case for the multiple source DA and domain generalization (DG) settings which are remarkably more complicated and sophisticated due to the involvement of multiple source domains and potential unavailability of target domain during training. In this paper, we develop novel upper-bounds for the target general loss which appeal us to define two kinds of domain-invariant representations. We further study the pros and cons as well as the trade-offs of enforcing learning each domain-invariant representation. Finally, we conduct experiments to inspect the trade-off of these representations for offering practical hints regarding how to use them in practice and explore other interesting properties of our developed theory.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experimental results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show that the complexity of the Sinkhorn algorithm for finding an $\varepsilon$-approximate solution to the UOT problem is of order $\widetilde{\mathcal{O}}(n^2/ \varepsilon)$. To the best of our knowledge, this complexity is better than the best known complexity upper bound of the Sinkhorn algorithm for solving the Optimal Transport (OT) problem, which is of order $\widetilde{\mathcal{O}}(n^2/\varepsilon^2)$. Our proof technique is based on the geometric convergence rate of the Sinkhorn updates to the optimal dual solution of the entropic regularized UOT problem and scaling properties of the primal solution. It is also different from the proof technique used to establish the complexity of the Sinkhorn algorithm for approximating the OT problem since the UOT solution does not need to meet the marginal constraints of the measures.

We propose a new formulation for learning generative adversarial networks (GANs) using optimal transport cost (the general form of Wasserstein distance) as the objective criterion to measure the dissimilarity between target distribution and learned distribution. Our formulation is based on the general form of the Kantorovich duality which is applicable to optimal transport with a wide range of cost functions that are not necessarily metric. To make optimising this duality form amenable to gradient-based methods, we employ a function that acts as an amortised optimiser for the innermost optimisation problem. Interestingly, the amortised optimiser can be viewed as a mover since it strategically shifts around data points. The resulting formulation is a sequential min-max-min game with 3 players: the generator, the critic, and the mover where the new player, the mover, attempts to fool the critic by shifting the data around. Despite involving three players, we demonstrate that our proposed formulation can be trained reasonably effectively via a simple alternative gradient learning strategy. Compared with the existing Lipschitz-constrained formulations of Wasserstein GAN on CIFAR-10, our model yields significantly better diversity scores than weight clipping and comparable performance to gradient penalty method.

Generative Adversarial Networks (GANs) are a powerful class of deep generative models. In this paper, we extend GAN to the problem of generating data that are not only close to a primary data source but also required to be different from auxiliary data sources. For this problem, we enrich both GANs' formulations and applications by introducing pushing forces that thrust generated samples away from given auxiliary data sources. We term our method Push-and-Pull GAN (P2GAN). We conduct extensive experiments to demonstrate the merit of P2GAN in two applications: generating data with constraints and addressing the mode collapsing problem. We use CIFAR-10, STL-10, and ImageNet datasets and compute Fréchet Inception Distance to evaluate P2GAN's effectiveness in addressing the mode collapsing problem. The results show that P2GAN outperforms the state-of-the-art baselines. For the problem of generating data with constraints, we show that P2GAN can successfully avoid generating specific features such as black hair.

Embed-to-control (E2C) is a model for solving high-dimensional optimal control problems by combining variational auto-encoders with locally-optimal controllers. However, the E2C model suffers from two major drawbacks: 1) its objective function does not correspond to the likelihood of the data sequence and 2) the variational encoder used for embedding typically has large variational approximation error, especially when there is noise in the system dynamics. In this paper, we present a new model for learning robust locally-linear controllable embedding (RCE). Our model directly estimates the predictive conditional density of the future observation given the current one, while introducing the bottleneck between the current and future observations. Although the bottleneck provides a natural embedding candidate for control, our RCE model introduces additional specific structures in the generative graphical model so that the model dynamics can be robustly linearized. We also propose a principled variational approximation of the embedding posterior that takes the future observation into account, and thus, makes the variational approximation more robust against the noise. Experimental results show that RCE outperforms the E2C model, and does so significantly when the underlying dynamics is noisy.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

We introduce a new framework for training deep generative models for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input x and target y, where both are high-dimensional. Crucially, we propose a new hybrid training method that blends the conditional generative model with a joint generative model. Hybrid blending is the key to effective training of the BCDE, which avoids overfitting and provides a novel mechanism for leveraging unlabeled data. We show that our hybrid training procedure enables models to achieve competitive results in the MNIST quadrant prediction task in the fully-supervised setting, and sets new benchmarks in the semi-supervised regime for MNIST, SVHN, and CelebA.

A typical online kernel learning method faces two fundamental issues: the complexity in dealing with a huge number of observed data points (a.k.a the curse of kernelization) and the difficulty in learning kernel parameters, which often assumed to be fixed. Random Fourier feature is a recent and effective approach to address the former by approximating the shift-invariant kernel function via Bocher's theorem, and allows the model to be maintained directly in the random feature space with a fixed dimension, hence the model size remains constant w.r.t. data size. We further introduce in this paper the reparameterized random feature (RRF), a random feature framework for large-scale online kernel learning to address both aforementioned challenges. Our initial intuition comes from the so-called "reparameterization trick" [Kingma et al., 2014] to lift the source of randomness of Fourier components to another space which can be independently sampled, so that stochastic gradient of the kernel parameters can be analytically derived. We develop a well-founded underlying theory for our method, including a general way to reparameterize the kernel, and a new tighter error bound on the approximation quality. This view further inspires a direct application of stochastic gradient descent for updating our model under an online learning setting. We then conducted extensive experiments on several large-scale datasets where we demonstrate that our work achieves state-of-the-art performance in both learning efficacy and efficiency.

We propose a general framework for discriminative Bayesian nonparametric clustering to promote the inter-discrimination among the learned clusters in a fully Bayesian nonparametric (BNP) manner. Our method combines existing BNP clustering and discriminative models by enforcing latent cluster indices to be consistent with the predicted labels resulted from probabilistic discriminative model. This formulation results in a well-defined generative process wherein we can use either logistic regression or SVM for discrimination. Using the proposed framework, we develop two novel discriminative BNP variants: the discriminative Dirichlet process mixtures, and the discriminative-state infinite HMMs for sequential data. We develop efficient data-augmentation Gibbs samplers for posterior inference. Extensive experiments in image clustering and dynamic location clustering demonstrate that by encouraging discrimination between induced clusters, our model enhances the quality of clustering in comparison with the traditional generative BNP models.

Matrix factorization (MF) collaborative filtering is an effective and widely used method in recommendation systems. However, the problem of finding an optimal trade-off between exploration and exploitation (otherwise known as the bandit problem), a crucial problem in collaborative filtering from cold-start, has not been previously addressed.In this paper, we present a novel algorithm for online MF recommendation that automatically combines finding the most relevantitems with exploring new or less-recommended items.Our approach, called Particle Thompson Sampling for Matrix-Factorization, is based on the general Thompson sampling framework, but augmented with a novel efficient online Bayesian probabilistic matrix factorization method based on the Rao-Blackwellized particle filter.Extensive experiments in collaborative filtering using several real-world datasets demonstrate that our proposed algorithm significantly outperforms the current state-of-the-arts.

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-measure with a nested structure to accommodate content and context observations at multiple levels. The proposed model possesses properties that link the nested Dirichlet processes (nDP) and the Dirichlet process mixture models (DPM) in an interesting way: integrating out all contents results in the DPM over contexts, whereas integrating out group-specific contexts results in the nDP mixture over content variables. We provide a Polya-urn view of the model and an efficient collapsed Gibbs inference procedure. Extensive experiments on real-world datasets demonstrate the advantage of utilizing context information via our model in both text and image domains.

The presence of non-symmetric evidence has been a barrier for the application of lifted inference since the evidence destroys the symmetry of the first-order probabilistic model. In the extreme case, if distinct soft evidence is obtained about each individual object in the domain then, often, all current exact lifted inference methods reduce to traditional inference at the ground level. However, it is of interest to ask whether the symmetry of the model itself before evidence is obtained can be exploited. We present new results showing that this is, in fact, possible. In particular, we show that both exact maximum a posteriori (MAP) and marginal inference can be lifted for the case of distinct soft evidence on a unary Markov Logic predicate. Our methods result in efficient procedures for MAP and marginal inference for a class of graphical models previously thought to be intractable.

Aggregate factors (that is, those based on aggregate functions such as SUM, AVERAGE, AND etc.) in probabilistic relational models can compactly represent dependencies among a large number of relational random variables. However, propositional inference on a factor aggregating n k-valued random variables into an r-valued result random variable is O(r k 2n). Lifted methods can ameliorate this to O(r nk) in general and O(r k log n) for commutative associative aggregators. In this paper, we propose (a) an exact solution constant in n when k = 2 for certain aggregate operations such as AND, OR and SUM, and (b) a close approximation for inference with aggregate factors with time complexity constant in n. This approximate inference involves an analytical solution for some operations when k > 2. The approximation is based on the fact that the typically used aggregate functions can be represented by linear constraints in the standard (k –1)-simplex in Rk where k is the number of possible values for random variables. This includes even aggregate functions that are commutative but not associative (e.g., the MODE operator that chooses the most frequent value). Our algorithm takes polynomial time in k (which is only 2 for binary variables) regardless of r and n, and the error decreases as n increases. Therefore, for most applications (in which a close approximation suffices) our algorithm is a much more efficient solution than existing algorithms. We present experimental results supporting these claims. We also present a (c) third contribution which further optimizes aggregations over multiple groups of random variables with distinct distributions.

This work addresses the issue of Bayesian robustness in the multivariate normal model when the prior covariance matrix is not completely specified, but rather is described in terms of positive semi-definite bounds. This occurs in situations where, for example, the only prior information available is the bound on the diagonal of the covariance matrix derived from some physical constraints, and that the covariance matrix is positive semi-definite, but otherwise arbitrary. Under the conditional Gamma-minimax principle, previous work by DasGupta and Studden shows that an analytically exact solution is readily available for a special case where the bound difference is a scaled identity. The goal in this work is to consider this problem for general positive definite matrices. The contribution in this paper is a theoretical study of the geometry of the minimax problem. Extension of previous results to a more general case is shown and a practical algorithm that relies on semi-definite programming and the convexity of the minimax formulation is derived. Although the algorithm is numerically exact for up to the bivariate case, its exactness for other cases remains open. Numerical studies demonstrate the accuracy of the proposed algorithm and the robustness of the minimax solution relative to standard and recently proposed methods.

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms for learning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.

Analysis of massive track datasets is a challenging problem, especially when examining n-way relations inherent in social networks. In this paper, we use the Mitsubishi track database to examine the usefulness of three types of interaction features observable in tracklet networks. We explore ways in which social network information can be extracted and visualized using a statistical sampling of these features from a very large track dataset, with very little ground truth or outside knowledge. Special attention is given to methods that are likely to scale well beyond the size of the Mitsubishi dataset.

Recognising behaviours of multiple people, especially high-level behaviours, is an important task in surveillance systems. When the reliable assignment of people to the set of observations is unavailable, this task becomes complicated. To solve this task, we present an approach, in which the hierarchical hidden Markov model (HHMM) is used for modeling the behaviour of each person and the joint probabilistic data association filters (JPDAF) is applied for data association. The main contributions of this paper lie in the integration of multiple HHMMs for recognising high-level behaviours of multiple people and the construction of the Rao-Blackwellised particle filters (RBPF) for approximate inference. Preliminary experimental results in a real environment show the robustness of our integrated method in behaviour recognition and its advantage over the use of Kalman filter in tracking people. 1

Activity recognition is an important issue in building intelligent monitoring systems. We address the recognition of multilevel activities in this paper via a conditional Markov random field (MRF), known as the dynamic conditional random field (DCRF). Parameter estimation in general MRFs using maximum likelihood is known to be computationally challenging (except for extreme cases), and thus we propose an efficient boosting-based algorithm AdaBoost.MRF for this task. Distinct from most existing work, our algorithm can handle hidden variables (missing labels) and is particularly attractive for smarthouse domains where reliable labels are often sparsely observed. Furthermore, our method works exclusively on trees and thus is guaranteed to converge. We apply the AdaBoost.MRF algorithmto a home video surveillance application and demonstrate its efficacy.

This paper addresses the problem of learning and recognizing human activities of daily living (ADL), which is an important research issue in building a pervasive and smart environment. In dealing with ADL, we argue that it is beneficial to exploit both the inherent hierarchical organization of the activities and their typical duration. To this end, we introduce the switching hidden semi-markov model (S-HSMM), a two-layered extension of the hidden semi-Markov model (HSMM) for the modeling task. Activities are modeled in the S-HSMM in two ways: the bottom layer represents atomic activities and their duration using HSMMs; the top layer represents a sequence of high-level activities where each high-level activity is made of a sequence of atomic activities. We consider two methods for modeling duration: the classic explicit duration model using multinomial distribution, and the novel use of the discrete Coxian distribution. In addition, we propose an effective scheme to detect abnormality without the need for training on abnormal data. Experimental results show that the S-HSMM performs better than existing models including the flat HSMM and the hierarchical hidden Markov model in both classification and abnormality detection tasks, alleviating the need for presegmented training data. Furthermore, our discrete Coxian duration model yields better computation time and generalization error than the classic explicit duration model.

Directly modeling the inherent hierarchy and shared structures of human behaviors, we present an application of the hierarchical hidden Markov model (HHMM) for the problem of activity recognition. We argue that to robustly model and recognize complex human activities, it is crucial to exploit both the natural hierarchical decomposition and shared semantics embedded in the movement trajectories. To this end, we propose the use of the HHMM, a rich stochastic model that has been recently extended to handle shared structures, for representing and recognizing a set of complex indoor activities. Furthermore, in the need of real-time recognition, we propose a Rao-Blackwellised particle filter (RBPF) that efficiently computes the filtering distribution at a constant time complexity for each new observation arrival. The main contributions of this paper lie in the application of the shared-structure HHMM, the estimation of the model's parameters at all levels simultaneously, and a construction of an RBPF approximate inference scheme. The experimental results in a real-world environment have confirmed our belief that directly modeling shared structures not only reduces computational cost, but also improves recognition accuracy when compared with the tree HHMM and the flat HMM.

In this paper we introduce a probabilistic framework to exploit hierarchy, structure sharing and duration information for topic transition detection in videos. Our probabilistic detection framework is a combination of a shot classification step and a detection phase using hierarchical probabilistic models. We consider two models in this paper: the extended Hierarchical Hidden Markov Model (HHMM) and the Coxian Switching Hidden semi-Markov Model (S-HSMM) because they allow the natural decomposition of semantics in videos, including shared structures, to be modeled directly, and thus enable efficient inference and reduce the sample complexity in learning. Additionally, the S-HSMM allows the duration information to be incorporated, consequently the modeling of long-term dependencies in videos is enriched through both hierarchical and duration modeling. Furthermore, the use of Coxian distribution in the S-HSMM makes it tractable to deal with long sequences in video. Our experimentation of the proposed framework on twelve educational and training videos shows that both models outperform the baseline cases (flat HMM and HSMM) and performances reported in earlier work in topic detection. The superior performance of the S-HSMM over the HHMM verifies our belief that the duration information is an important factor in video content modeling.

We present results on the recognition of intentional human gestures for video annotation and retrieval. We define a gesture as a particular, repeatable, human movement having a predefined meaning. An obvious application of the work is in sports video annotation where umpire gestures indicate specific events. Our approach is to augment video with data obtained from accelerometers worn as wrist bands by one or more officials. We present the recognition performance using a Hidden Markov Model approach for gesture modeling with both isolated gestures and gestures segmented from a stream.

The recognition of activities from sensory data is important in advanced surveillance systems to enable prediction of high-level goals and intentions of the target under surveillance. The problem is complicated by sensory noise and complex activity spanning large spatial and temporal extents. The paper presents a system for recognizing high-level human activities from multi-camera video data in complex spatial environments. The Abstract Hidden Markov mEmory Model (AHMEM) is used to deal with noise and scalability. The AHMEM is an extension of the Abstract Hidden Markov Model (AHMM) that allows us to represent a richer class of both state-dependent and context-free behaviors. The model also supports integration with low-level sensory models and efficient probabilistic inference. We present experimental results showing the ability of the system to perform real-time monitoring and recognition of complex behaviors of people from observing their trajectories within a real, complex indoor environment.

This work constitutes the first attempt to extract an important narrative structure, the 3-Act story telling paradigm, in film. This narrative structure is prevalent in the domain of film as it forms the foundation and framework in which the film can be made to function as an effective tool for story telling, and its extraction is a vital step in automatic content management for film data. A novel act boundary likelihood function for Act 1 is derived using a Bayesian formulation under guidance from film grammar, tested under many configurations and the results are reported for experiments involving 25 full length movies. The formulation is shown to be a useful tool in both the automatic and semi-interactive setting for semantic analysis of film.

Seeking to extend the functional capability of the elderly, we explore the use of probabilistic methods to learn and recognise human activity in order to provide monitoring support. We propose a novel approach to learning the hierarchical structure of sequences of human actions through the application of the hierarchical hidden Markov model (HHMM). Experimental results are presented for learning and recognising sequences of typical activities in a home.

The paper presents a method for finding and classifying objects within real-world scenes by using the activity of humans interacting with these objects to infer the object's identity. Objects are labelled using evidence accumulated over time and multiple instances of human interactions. This approach is inspired by the problems and opportunities that exist in recognition tasks for intelligent homes, namely cluttered, wide-angle views coupled with significant and repeated human activity within the scene. The advantages of such an approach include the ability to detect salient objects in a cluttered scene, independent of the object's physical structure, adapt to changes in the scene and resolve conflicts in labels by weight of past evidence. This initial investigation seeks to label chairs and open floor spaces by recognising activities such as walking and silting. Findings show that the approach can locate objects with a reasonably high degree of accuracy, with occlusions of the human actor being a significant aid in reducing over-labelling.

In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an efficient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.

In this paper, we consider the problem of tracking an object and predicting the object's future trajectory in a wide-area environment, with complex spatial layout and the use of multiple sensors/cameras. To solve this problem, there is a need for representing the dynamic and noisy data in the tracking tasks, and dealing with them at different levels of detail. We employ the Abstract Hidden Markov Models (AHMM), an extension of the well-known Hidden Markov Model (HMM) and a special type of Dynamic Probabilistic Network (DPN), as our underlying representation framework. The AHMM allows us to explicitly encode the hierarchy of connected spatial locations, making it scalable to the size of the environment being modeled. We describe an application for tracking human movement in an office-like spatial layout where the AHMM is used to track and predict the evolution of object trajectories at different levels of detail.

Surveillance in wide-area spatial environments is characterised by complex spatial layouts, large state space, and the use of multiple cameras/sensors. To solve this problem, there is a need for representing the dynamic and noisy data in the tracking tasks, and dealing with them at different levels of detail. This requirement is particularly suited to the layered dynamic probabilistic network (LDPN), a special type of dynamic probabilistic network. In this paper, we propose the use of LDPN as the integrated framework for tracking in wide-area environments. We illustrate, with the help of a synthetic tracking scenario, how the parameters of the LDPN can be estimated from training data, and then used to draw predictions and answer queries about unseen tracks at various levels of detail.

In applications such as tracking and surveillance in large spatial environments, there is a need for representing dynamic and noisy data and at the same time dealing with them at different levels of detail. In the spatial domain, there has been work dealing with these two issues separately, however, there is no existing common framework for dealing with both of them. In this paper, we propose a new representation framework called the Layered Dynamic Probabilistic Network (LDPN), a special type of Dynamic Probabilistic Network (DPN), capable of handling uncertainty and representing spatial data at various levels of detail. The framework is thus particularly suited to applications in wide-area environments which are characterised by large region size, complex spatial layout and multiple sensors/cameras. For example, a building has three levels: entry/exit to the building, entry/exit between rooms and moving within rooms. To avoid the problem of a relatively large state space associated with a large spatial environment, the LDPN explicitly encodes the hierarchy of connected spatial locations, making it scalable to the size of the environment being modelled. There are three main advantages of the LDPN. First, the reduction in state space makes it suitable for dealing with wide area surveillance involving multiple sensors. Second, it offers a hierarchy of intervals for indexing temporal data. Lastly, the explicit representation of intermediate sub-goals allows for the extension of the framework to easily represent group interactions by allowing coupling between sub-goal layers of different individuals or objects. We describe an adaptation of the likelihood sampling inference scheme for the LDPN, and illustrate its use in a hypothetical surveillance scenario.

In multi-agent systems, most of the time, an agent does not have complete information about the preferences and decision making processes of other agents. This prevents even the cooperative agents from making coordinated choices, purely due to their ignorance of what other want. To overcome this problem, traditional coordination methods rely heavily on inter-agent communication, and thus become very inefficient when communication is costly or simply not desirable (e.g. to preserve privacy). In this paper, we propose the use of learning to complement communication in acquiring knowledge about other agents. We augment the communication-intensive negotiating agent architecture with a learning module, implemented as a Bayesian classifier. This allows our agents to incrementally update models of other agents' preferences from past negotiations with them. Based on these models, the agents can make sound predictions about others' preferences, thus reducing the need for communication in their future interactions.