Reshad Hosseini

Mohammad Pasande, Reshad Hosseini, Babak Nadjar Araabi

Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges of common GMMs when faced with high-dimensional data and complex densities which often demand a large number of Gaussian components. However, the expectation-maximization algorithm for fitting flexibly-tied GMMs still encounters difficulties with streaming and very large dimensional data. To overcome these challenges, this paper suggests the use of first-order stochastic optimization algorithms. Specifically, we propose a new stochastic optimization algorithm on the manifold of orthogonal matrices. Through numerous empirical results on both synthetic and real datasets, we observe that stochastic optimization methods can outperform the expectation-maximization algorithm in terms of attaining better likelihood, needing fewer epochs for convergence, and consuming less time per each epoch.

Mohammad Hossein Nasseri, Mohammadreza Babaee, Hadi Moradi et al.

To overcome challenges in multiple object tracking task, recent algorithms use interaction cues alongside motion and appearance features. These algorithms use graph neural networks or transformers to extract interaction features that lead to high computation costs. In this paper, a novel interaction cue based on geometric features is presented aiming to detect occlusion and re-identify lost targets with low computational cost. Moreover, in most algorithms, camera motion is considered negligible, which is a strong assumption that is not always true and leads to ID Switch or mismatching of targets. In this paper, a method for measuring camera motion and removing its effect is presented that efficiently reduces the camera motion effect on tracking. The proposed algorithm is evaluated on MOT17 and MOT20 datasets and it achieves the state-of-the-art performance of MOT17 and comparable results on MOT20. The code is also publicly available.

Peyman Baghershahi, Reshad Hosseini, Hadi Moradi

Numerous Graph Neural Networks (GNNs) have been developed to tackle the challenge of Knowledge Graph Embedding (KGE). However, many of these approaches overlook the crucial role of relation information and inadequately integrate it with entity information, resulting in diminished expressive power. In this paper, we propose a novel knowledge graph encoder that incorporates tensor decomposition within the aggregation function of Relational Graph Convolutional Network (R-GCN). Our model enhances the representation of neighboring entities by employing projection matrices of a low-rank tensor defined by relation types. This approach facilitates multi-task learning, thereby generating relation-aware representations. Furthermore, we introduce a low-rank estimation technique for the core tensor through CP decomposition, which effectively compresses and regularizes our model. We adopt a training strategy inspired by contrastive learning, which relieves the training limitation of the 1-N method inherent in handling vast graphs. We outperformed all our competitors on two common benchmark datasets, FB15k-237 and WN18RR, while using low-dimensional embeddings for entities and relations.

Erfan Mirzaei, Seyed Pooya Shariatpanahi, Alireza Tavakoli et al.

Personalized AI-based services involve a population of individual reinforcement learning agents. However, most reinforcement learning algorithms focus on harnessing individual learning and fail to leverage the social learning capabilities commonly exhibited by humans and animals. Social learning integrates individual experience with observing others' behavior, presenting opportunities for improved learning outcomes. In this study, we focus on a social bandit learning scenario where a social agent observes other agents' actions without knowledge of their rewards. The agents independently pursue their own policy without explicit motivation to teach each other. We propose a free energy-based social bandit learning algorithm over the policy space, where the social agent evaluates others' expertise levels without resorting to any oracle or social norms. Accordingly, the social agent integrates its direct experiences in the environment and others' estimated policies. The theoretical convergence of our algorithm to the optimal policy is proven. Empirical evaluations validate the superiority of our social learning method over alternative approaches in various scenarios. Our algorithm strategically identifies the relevant agents, even in the presence of random or suboptimal agents, and skillfully exploits their behavioral information. In addition to societies including expert agents, in the presence of relevant but non-expert agents, our algorithm significantly enhances individual learning performance, where most related methods fail. Importantly, it also maintains logarithmic regret.

Alireza Salehi, Ehsan Karami, Sepehr Noey et al.

Anomaly detection identifies departures from expected behavior in safety-critical settings. When target-domain normal data are unavailable, zero-shot anomaly detection (ZSAD) leverages vision-language models (VLMs). However, CLIP's coarse image-text alignment limits both localization and detection due to (i) spatial misalignment and (ii) weak sensitivity to fine-grained anomalies; prior work compensates with complex auxiliary modules yet largely overlooks the choice of backbone. We revisit the backbone and use TIPS-a VLM trained with spatially aware objectives. While TIPS alleviates CLIP's issues, it exposes a distributional gap between global and local features. We address this with decoupled prompts-fixed for image-level detection and learnable for pixel-level localization-and by injecting local evidence into the global score. Without CLIP-specific tricks, our TIPS-based pipeline improves image-level performance by 1.1-3.9% and pixel-level by 1.5-6.9% across seven industrial datasets, delivering strong generalization with a lean architecture. Code is available at github.com/AlirezaSalehy/Tipsomaly.

Mohammad Mahdi Afrasiabi, Reshad Hosseini, Aliazam Abbasfar

Super-resolution is the process of obtaining a high-resolution image from one or more low-resolution images. Single image super-resolution (SISR) and multi-frame super-resolution (MFSR) methods have been evolved almost independently for years. A neglected study in this field is the theoretical analysis of finding the optimum combination of SISR and MFSR. To fill this gap, we propose a novel theoretical analysis based on the iterative shrinkage and thresholding algorithm. We implement and compare several approaches for combining SISR and MFSR, and simulation results support the finding of our theoretical analysis, both quantitatively and qualitatively.

Ali Karimi, Zahra Mousavi Kouzehkanan, Reshad Hosseini et al.

This paper introduces a new loss function, OSM (One-Sided Margin), to solve maximum-margin classification problems effectively. Unlike the hinge loss, in OSM the margin is explicitly determined with corresponding hyperparameters and then the classification problem is solved. In experiments, we observe that using OSM loss leads to faster training speeds and better accuracies than binary and categorical cross-entropy in several commonly used deep models for classification and optical character recognition problems. OSM has consistently shown better classification accuracies over cross-entropy and hinge losses for small to large neural networks. it has also led to a more efficient training procedure. We achieved state-of-the-art accuracies for small networks on several benchmark datasets of CIFAR10(98.82\%), CIFAR100(91.56\%), Flowers(98.04\%), Stanford Cars(93.91\%) with considerable improvements over other loss functions. Moreover, the accuracies are rather better than cross-entropy and hinge loss for large networks. Therefore, we strongly believe that OSM is a powerful alternative to hinge and cross-entropy losses to train deep neural networks on classification tasks.

Yasaman Haghbin, Hadi Moradi, Reshad Hosseini

One of the growing trends in machine learning is the use of data generation techniques, since the performance of machine learning models is dependent on the quantity of the training dataset. However, in many real-world applications, particularly in medical and low-resource domains, collecting large datasets is challenging due to resource constraints, which leads to overfitting and poor generalization. This study introduces FICAug, a novel feature-to-image data augmentation framework designed to improve model generalization under limited data conditions by generating structured synthetic samples. FICAug first operates in the feature space, where original data are clustered using the k-means algorithm. Within pure-label clusters, synthetic data are generated through Gaussian sampling to increase diversity while maintaining label consistency. These synthetic features are then projected back into the image domain using a generative neural network, and a convolutional neural network is trained on the reconstructed images to learn enhanced representations. Experimental results demonstrate that FICAug significantly improves classification accuracy. In feature space, it achieved a cross-validation accuracy of 84.09%, while training a ResNet-18 model on the reconstructed images further boosted performance to 88.63%, illustrating the effectiveness of the proposed framework in extracting new and task-relevant features.

Seyedeh Fatemeh Razavi, Mohammad Mahdi Mehmanchi, Reshad Hosseini et al.

Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models providing a tractable density estimation via dimension-preserving invertible transformations. Conventional normalizing flows are prone to fail in out-of-distribution detection, because of the well-known curse of dimensionality problem of the likelihood-based models. To solve the problem of likelihood-based models, some works try to modify likelihood for example by incorporating a data complexity measure. We observed that these modifications are still insufficient. According to the manifold hypothesis, real-world data often lie on a low-dimensional manifold. Therefore, we proceed by estimating the density on a low-dimensional manifold and calculating a distance from the manifold as a measure for out-of-distribution detection. We propose a powerful criterion that combines this measure with the modified likelihood measure based on data complexity. Extensive experimental results show that incorporating manifold learning while accounting for the estimation of data complexity improves the out-of-distribution detection ability of normalizing flows. This improvement is achieved without modifying the model structure or using auxiliary out-of-distribution data during training.

Seyedeh Fatemeh Razavi, Mohammad Mahdi Mehmanchi, Reshad Hosseini et al.

Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one interesting question arises: $\textit{"Can we find sub-manifold(s) of data in normalizing flows and estimate the density of the data on the sub-manifold(s)?"}$. In this paper, we introduce two approaches, namely per-pixel penalized log-likelihood and hierarchical training, to answer the mentioned question. We propose a single-step method for joint manifold learning and density estimation by disentangling the transformed space obtained by normalizing flows to manifold and off-manifold parts. This is done by a per-pixel penalized likelihood function for learning a sub-manifold of the data. Normalizing flows assume the transformed data is Gaussianizationed, but this imposed assumption is not necessarily true, especially in high dimensions. To tackle this problem, a hierarchical training approach is employed to improve the density estimation on the sub-manifold. The results validate the superiority of the proposed methods in simultaneous manifold learning and density estimation using normalizing flows in terms of generated image quality and likelihood.

Alireza Salehi, Mohammadreza Salehi, Reshad Hosseini et al.

Anomaly Detection involves identifying deviations from normal data distributions and is critical in fields such as medical diagnostics and industrial defect detection. Traditional AD methods typically require the availability of normal training samples; however, this assumption is not always feasible. Recently, the rich pretraining knowledge of CLIP has shown promising zero-shot generalization in detecting anomalies without the need for training samples from target domains. However, CLIP's coarse-grained image-text alignment limits localization and detection performance for fine-grained anomalies due to: (1) spatial misalignment, and (2) the limited sensitivity of global features to local anomalous patterns. In this paper, we propose Crane which tackles both problems. First, we introduce a correlation-based attention module to retain spatial alignment more accurately. Second, to boost the model's awareness of fine-grained anomalies, we condition the learnable prompts of the text encoder on image context extracted from the vision encoder and perform a local-to-global representation fusion. Moreover, our method can incorporate vision foundation models such as DINOv2 to further enhance spatial understanding and localization. The key insight of Crane is to balance learnable adaptations for modeling anomalous concepts with non-learnable adaptations that preserve and exploit generalized pretrained knowledge, thereby minimizing in-domain overfitting and maximizing performance on unseen domains. Extensive evaluation across 14 diverse industrial and medical datasets demonstrates that Crane consistently improves the state-of-the-art ZSAD from 2% to 28%, at both image and pixel levels, while remaining competitive in inference speed. The code is available at https://github.com/AlirezaSalehy/Crane.

Romina Oji, Seyedeh Fatemeh Razavi, Sajjad Abdi Dehsorkh et al.

In general, speech processing models consist of a language model along with an acoustic model. Regardless of the language model's complexity and variants, three critical pre-processing steps are needed in language models: cleaning, normalization, and tokenization. Among mentioned steps, the normalization step is so essential to format unification in pure textual applications. However, for embedded language models in speech processing modules, normalization is not limited to format unification. Moreover, it has to convert each readable symbol, number, etc., to how they are pronounced. To the best of our knowledge, there is no Persian normalization toolkits for embedded language models in speech processing modules, So in this paper, we propose an open-source normalization toolkit for text processing in speech applications. Briefly, we consider different readable Persian text like symbols (common currencies, #, @, URL, etc.), numbers (date, time, phone number, national code, etc.), and so on. Comparison with other available Persian textual normalization tools indicates the superiority of the proposed method in speech processing. Also, comparing the model's performance for one of the proposed functions (sentence separation) with other common natural language libraries such as HAZM and Parsivar indicates the proper performance of the proposed method. Besides, its evaluation of some Persian Wikipedia data confirms the proper performance of the proposed method.

Atefeh Irani, Maryam S. Mirian, Alex Lassooij et al.

Video-based assessment of motor symptoms in conditions such as Parkinson's disease (PD) offers a scalable alternative to in-clinic evaluations, but home-recorded videos introduce significant challenges, including visual degradation, inconsistent task execution, annotation noise, and domain shifts. We present HiLWS, a cascaded human-in-the-loop weak supervision framework for curating and annotating hand motor task videos from both clinical and home settings. Unlike conventional single-stage weak supervision methods, HiLWS employs a novel cascaded approach, first applies weak supervision to aggregate expert-provided annotations into probabilistic labels, which are then used to train machine learning models. Model predictions, combined with expert input, are subsequently refined through a second stage of weak supervision. The complete pipeline includes quality filtering, optimized pose estimation, and task-specific segment extraction, complemented by context-sensitive evaluation metrics that assess both visual fidelity and clinical relevance by prioritizing ambiguous cases for expert review. Our findings reveal key failure modes in home recorded data and emphasize the importance of context-sensitive curation strategies for robust medical video analysis.

Farshad Sangari Abiz, Reshad Hosseini, Babak N. Araabi

Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially in high-dimensional spaces. To address this challenge, Variational Sparse Coding (VSC) introduces a spike-and-slab prior distribution, resulting in sparse latent representations for each input. These sparse representations, characterized by a limited number of active dimensions, are inherently more interpretable. Despite this advantage, VSC falls short in providing structured interpretations across samples within the same class. Intuitively, samples from the same class are expected to share similar attributes while allowing for variations in those attributes. This expectation should manifest as consistent patterns of active dimensions in their latent representations, but VSC does not enforce such consistency. In this paper, we propose a novel approach to enhance the latent space interpretability by ensuring that the active dimensions in the latent space are consistent across samples within the same class. To achieve this, we introduce a new loss function that encourages samples from the same class to share similar active dimensions. This alignment creates a more structured and interpretable latent space, where each shared dimension corresponds to a high-level concept, or "factor." Unlike existing disentanglement-based methods that primarily focus on global factors shared across all classes, our method captures both global and class-specific factors, thereby enhancing the utility and interpretability of latent representations.

Amirhossein Mesbah, Reshad Hosseini, Seyed Pooya Shariatpanahi et al.

Reinforcement learning (RL) plays a major role in solving complex sequential decision-making tasks. Hierarchical and goal-conditioned RL are promising methods for dealing with two major problems in RL, namely sample inefficiency and difficulties in reward shaping. These methods tackle the mentioned problems by decomposing a task into simpler subtasks and temporally abstracting a task in the action space. One of the key components for task decomposition of these methods is subgoal discovery. We can use the subgoal states to define hierarchies of actions and also use them in decomposing complex tasks. Under the assumption that subgoal states are more unpredictable, we propose a free energy paradigm to discover them. This is achieved by using free energy to select between two spaces, the main space and an aggregation space. The $model \; changes$ from neighboring states to a given state shows the unpredictability of a given state, and therefore it is used in this paper for subgoal discovery. Our empirical results on navigation tasks like grid-world environments show that our proposed method can be applied for subgoal discovery without prior knowledge of the task. Our proposed method is also robust to the stochasticity of environments.

Peyman Baghershahi, Reshad Hosseini, Hadi Moradi

A few models have tried to tackle the link prediction problem, also known as knowledge graph completion, by embedding knowledge graphs in comparably lower dimensions. However, the state-of-the-art results are attained at the cost of considerably increasing the dimensionality of embeddings which causes scalability issues in the case of huge knowledge bases. Transformers have been successfully used recently as powerful encoders for knowledge graphs, but available models still have scalability issues. To address this limitation, we introduce a Transformer-based model to gain expressive low-dimensional embeddings. We utilize a large number of self-attention heads as the key to applying query-dependent projections to capture mutual information between entities and relations. Empirical results on WN18RR and FB15k-237 as standard link prediction benchmarks demonstrate that our model has favorably comparable performance with the current state-of-the-art models. Notably, we yield our promising results with a significant reduction of 66.9% in the dimensionality of embeddings compared to the five best recent state-of-the-art competitors on average.

Seyed-Mahdi Nasiri, Reshad Hosseini, Hadi Moradi

A viewing graph is a set of unknown camera poses, as the vertices, and the observed relative motions, as the edges. Solving the viewing graph is an essential step in a Structure-from-Motion procedure, where a set of relative motions is obtained from a collection of 2D images. Almost all methods in the literature solve for the rotations separately, through rotation averaging process, and use them for solving the positions. Obtaining positions is the challenging part because the translation observations only tell the direction of the motions. It becomes more challenging when the set of edges comprises pairwise translation observations between either near and far cameras. In this paper an iterative method is proposed that overcomes these issues. Also a method is proposed which obtains the rotations and positions simultaneously. Experimental results show the-state-of-the-art performance of the proposed methods.

Reza Godaz, Benyamin Ghojogh, Reshad Hosseini et al.

This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for numerical optimization in Euclidean spaces. Riemannian LBFGS (RLBFGS) is an extension of this method to Riemannian manifolds. RLBFGS involves computationally expensive vector transports as well as unfolding recursions using adjoint vector transports. In this article, we propose two mappings in the tangent space using the inverse second root and Cholesky decomposition. These mappings make both vector transport and adjoint vector transport identity and therefore isometric. Identity vector transport makes RLBFGS less computationally expensive and its isometry is also very useful in convergence analysis of RLBFGS. Moreover, under the proposed mappings, the Riemannian metric reduces to Euclidean inner product, which is much less computationally expensive. We focus on the Symmetric Positive Definite (SPD) manifolds which are beneficial in various fields such as data science and statistics. This work opens a research opportunity for extension of the proposed mappings to other well-known manifolds.

Seyed-Mahdi Nasiri, Reshad Hosseini, Hadi Moradi

Triangulation refers to the problem of finding a 3D point from its 2D projections on multiple camera images. For solving this problem, it is the common practice to use so-called optimal triangulation method, which we call the L2 method in this paper. But, the method can be optimal only if we assume no uncertainty in the camera parameters. Through extensive comparison on synthetic and real data, we observed that the L2 method is actually not the best choice when there is uncertainty in the camera parameters. Interestingly, it can be observed that the simple mid-point method outperforms other methods. Apart from its high performance, the mid-point method has a simple closed formed solution for multiple camera images while the L2 method is hard to be used for more than two camera images. Therefore, in contrast to the common practice, we argue that the simple mid-point method should be used in structure-from-motion applications where there is uncertainty in camera parameters.

Reza Godaz, Reza Monsefi, Faezeh Toutounian et al.

In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan bidiagonalization (GK-bidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two various image datasets of MNIST and USPS.

Aida Khozaei, Hadi Moradi, Reshad Hosseini

There are partially separable data types that make classification tasks very hard. In other words, only parts of the data are informative meaning that looking at the rest of the data would not give any distinguishable hint for classification. In this situation, the typical assumption of having the whole labeled data as an informative unit set for classification does not work. Consequently, typical classification methods with the mentioned assumption fail in such a situation. In this study, we propose a framework for the classification of partially separable data types that are not classifiable using typical methods. An algorithm based on the framework is proposed that tries to detect separable subgroups of the data using an iterative clustering approach. Then the detected subgroups are used in the classification process. The proposed approach was tested on a real dataset for autism screening and showed its capability by distinguishing children with autism from normal ones, while the other methods failed to do so.

Mohammad Hossein Nasseri, Hadi Moradi, Reshad Hosseini et al.

Multiple object tracking is a challenging problem in computer vision due to difficulty in dealing with motion prediction, occlusion handling, and object re-identification. Many recent algorithms use motion and appearance cues to overcome these challenges. But using appearance cues increases the computation cost notably and therefore the speed of the algorithm decreases significantly which makes them inappropriate for online applications. In contrast, there are algorithms that only use motion cues to increase speed, especially for online applications. But these algorithms cannot handle occlusions and re-identify lost objects. In this paper, a novel online multiple object tracking algorithm is presented that only uses geometric cues of objects to tackle the occlusion and reidentification challenges simultaneously. As a result, it decreases the identity switch and fragmentation metrics. Experimental results show that the proposed algorithm could decrease identity switch by 40% and fragmentation by 28% compared to the state of the art online tracking algorithms. The code is also publicly available.

Milad Ghorbani, Reshad Hosseini, Seyed Pooya Shariatpanahi et al.

In large-scale problems, standard reinforcement learning algorithms suffer from slow learning speed. In this paper, we follow the framework of using subspaces to tackle this problem. We propose a free-energy minimization framework for selecting the subspaces and integrate the policy of the state-space into the subspaces. Our proposed free-energy minimization framework rests upon Thompson sampling policy and behavioral policy of subspaces and the state-space. It is therefore applicable to a variety of tasks, discrete or continuous state space, model-free and model-based tasks. Through a set of experiments, we show that this general framework highly improves the learning speed. We also provide a convergence proof.

Zahra Mousavi Kouzehkanan, Reshad Hosseini, Babak Nadjar Araabi

Many edge and contour detection algorithms give a soft-value as an output and the final binary map is commonly obtained by applying an optimal threshold. In this paper, we propose a novel method to detect image contours from the extracted edge segments of other algorithms. Our method is based on an undirected graphical model with the edge segments set as the vertices. The proposed energy functions are inspired by the surround modulation in the primary visual cortex that help suppressing texture noise. Our algorithm can improve extracting the binary map, because it considers other important factors such as connectivity, smoothness, and length of the contour beside the soft-values. Our quantitative and qualitative experimental results show the efficacy of the proposed method.

Seyedeh Fatemeh Razavi, Reshad Hosseini, Tina Behzad

The class of recurrent mixture density networks is an important class of probabilistic models used extensively in sequence modeling and sequence-to-sequence mapping applications. In this class of models, the density of a target sequence in each time-step is modeled by a Gaussian mixture model with the parameters given by a recurrent neural network. In this paper, we generalize recurrent mixture density networks by defining a Gaussian mixture model on a non-linearly transformed target sequence in each time-step. The non-linearly transformed space is created by normalizing flow. We observed that this model significantly improves the fit to image sequences measured by the log-likelihood. We also applied the proposed model on some speech and image data, and observed that the model has significant modeling power outperforming other state-of-the-art methods in terms of the log-likelihood.

Taraneh Younesian, Saeed Masoudnia, Reshad Hosseini et al.

Offline Signature Verification (OSV) remains a challenging pattern recognition task, especially in the presence of skilled forgeries that are not available during the training. This challenge is aggravated when there are small labeled training data available but with large intra-personal variations. In this study, we address this issue by employing an active learning approach, which selects the most informative instances to label and therefore reduces the human labeling effort significantly. Our proposed OSV includes three steps: feature learning, active learning, and final verification. We benefit from transfer learning using a pre-trained CNN for feature learning. We also propose SVM-based active learning for each user to separate his genuine signatures from the random forgeries. We finally used the SVMs to verify the authenticity of the questioned signature. We examined our proposed active transfer learning method on UTSig: A Persian offline signature dataset. We achieved near 13% improvement compared to the random selection of instances. Our results also showed 1% improvement over the state-of-the-art method in which a fully supervised setting with five more labeled instances per user was used.

Pourya Habib Zadeh, Reshad Hosseini, Suvrit Sra

One of the main drawbacks of deep neural networks, like many other classifiers, is their vulnerability to adversarial attacks. An important reason for their vulnerability is assigning high confidence to regions with few or even no feature points. By feature points, we mean a nonlinear transformation of the input space extracting a meaningful representation of the input data. On the other hand, deep-RBF networks assign high confidence only to the regions containing enough feature points, but they have been discounted due to the widely-held belief that they have the vanishing gradient problem. In this paper, we revisit the deep-RBF networks by first giving a general formulation for them, and then proposing a family of cost functions thereof inspired by metric learning. In the proposed deep-RBF learning algorithm, the vanishing gradient problem does not occur. We make these networks robust to adversarial attack by adding the reject option to their output layer. Through several experiments on the MNIST dataset, we demonstrate that our proposed method not only achieves significant classification accuracy but is also very resistant to various adversarial attacks.

S. M. Nasiri, Reshad Hosseini, Hadi Moradi

Pose Graph Optimization (PGO) is an important non-convex optimization problem and is the state-of-the-art formulation for SLAM in robotics. It also has applications like camera motion estimation, structure from motion and 3D reconstruction in machine vision. Recent researches have shown the importance of good initialization to bootstrap well-known iterative PGO solvers to converge to good solutions. The state-of-the-art initialization methods, however, works in low noise or eventually moderate noise problems, and they fail in challenging problems with high measurement noise. Consequently, iterative methods may get entangled in local minima in high noise scenarios. In this paper we present an initialization method which uses orientation measurements and then present a convergence analysis of our iterative algorithm. We show how the algorithm converges to global optima in noise-free cases and also obtain a bound for the difference between our result and the optimum solution in scenarios with noisy measurements. We then present our second algorithm that uses both relative orientation and position measurements to obtain a more accurate least squares approximation of the problem that is again solved iteratively. In the convergence proof, a structural coefficient arises that has important influence on the basin of convergence. Interestingly, simulation results show that this coefficient also affects the performance of other solvers and so it can indicate the complexity of the problem. Experimental results show the excellent performance of the proposed initialization algorithm, specially in high noise scenarios.

Maryam Hashemzadeh, Reshad Hosseini, Majid Nili Ahmadabadi

Due to the lack of enough generalization in the state-space, common methods in Reinforcement Learning (RL) suffer from slow learning speed especially in the early learning trials. This paper introduces a model-based method in discrete state-spaces for increasing learning speed in terms of required experience (but not required computational time) by exploiting generalization in the experiences of the subspaces. A subspace is formed by choosing a subset of features in the original state representation (full-space). Generalization and faster learning in a subspace are due to many-to-one mapping of experiences from the full-space to each state in the subspace. Nevertheless, due to inherent perceptual aliasing in the subspaces, the policy suggested by each subspace does not generally converge to the optimal policy. Our approach, called Model Based Learning with Subspaces (MoBLeS), calculates confidence intervals of the estimated Q-values in the full-space and in the subspaces. These confidence intervals are used in the decision making, such that the agent benefits the most from the possible generalization while avoiding from detriment of the perceptual aliasing in the subspaces. Convergence of MoBLeS to the optimal policy is theoretically investigated. Additionally, we show through several experiments that MoBLeS improves the learning speed in the early trials.

Reshad Hosseini, Suvrit Sra

We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which is its ability to fulfill positive definiteness constraints in closed form is of key importance. We propose an alternative to EM by appealing to the rich Riemannian geometry of positive definite matrices, using which we cast Gmm parameter estimation as a Riemannian optimization problem. Surprisingly, such an out-of-the-box Riemannian formulation completely fails and proves much inferior to EM. This motivates us to take a closer look at the problem geometry, and derive a better formulation that is much more amenable to Riemannian optimization. We then develop (Riemannian) batch and stochastic gradient algorithms that outperform EM, often substantially. We provide a non-asymptotic convergence analysis for our stochastic method, which is also the first (to our knowledge) such global analysis for Riemannian stochastic gradient. Numerous empirical results are included to demonstrate the effectiveness of our methods.

Pourya Habib Zadeh, Reshad Hosseini, Suvrit Sra

We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution consistently attains higher classification accuracy.

Reshad Hosseini, Mohamadreza Mash'al

Mixture models are powerful statistical models used in many applications ranging from density estimation to clustering and classification. When dealing with mixture models, there are many issues that the experimenter should be aware of and needs to solve. The MixEst toolbox is a powerful and user-friendly package for MATLAB that implements several state-of-the-art approaches to address these problems. Additionally, MixEst gives the possibility of using manifold optimization for fitting the density model, a feature specific to this toolbox. MixEst simplifies using and integration of mixture models in statistical models and applications. For developing mixture models of new densities, the user just needs to provide a few functions for that statistical distribution and the toolbox takes care of all the issues regarding mixture models. MixEst is available at visionlab.ut.ac.ir/mixest and is fully documented and is licensed under GPL.

Reshad Hosseini, Suvrit Sra

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation of manifold optimization, however, fails spectacularly: it converges to the same solution but vastly slower. Driven by intuition from manifold convexity, we then propose a reparamerization that has remarkable empirical consequences. It makes manifold optimization not only match EM---a highly encouraging result in itself given the poor record nonlinear programming methods have had against EM so far---but also outperform EM in many practical settings, while displaying much less variability in running times. We further highlight the strengths of manifold optimization by developing a somewhat tuned manifold LBFGS method that proves even more competitive and reliable than existing manifold optimization tools. We hope that our results encourage a wider consideration of manifold optimization for parameter estimation problems.

Reshad Hosseini, Suvrit Sra, Lucas Theis et al.

We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and converge to global optima despite nonconvexity. Moreover, they turn out to be much faster than both a well-known iterative algorithm of Kent & Tyler (1991) and sophisticated manifold optimization algorithms. Subsequently, we invoke our ML algorithms as subroutines for estimating parameters of a mixture of EGDs. We illustrate our methods by applying them to model natural image statistics---the proposed EGD mixture model yields the most parsimonious model among several competing approaches.