arXiv subjects

Andras Lorincz

Publications and source records attributed to Andras Lorincz.

At least 19 recordsLinked to original sources

arXiv2026

Filtrations on D-modules and multiplicities of roots of Bernstein-Sato polynomials

In this paper, we relate multiplicities of Bernstein--Sato-type polynomials with respect to a holomorphic function f to several singularity invariants. First, we introduce certain ``mod'' b-functions and show that they characterize the weight filtration on the localization of a simple regular holonomic D-module along f, and we provide an algorithm to compute them. Second, we show that they can be approximated by the multiplicities of roots of power b-functions (the b-functions with respect to powers of f). Further, we give a sharp upper bound for the Hodge level of elements given by a certain sum of such multiplicities. Next, we give an effective asymptotic solution to the Gelfand problem by determining an explicit threshold after which every integer shift of a root of b_f(s) is a pole of the Archimedean zeta function of f. We also show that the order of these poles is equal to the nilpotency index of the logarithmic monodromy operator, which we further express as the limit of the multiplicities of roots of power b-functions. We define several filtrations, relating them to the weight and Hodge filtrations, based upon which we leave some open questions that we address in the affirmative in the case when f has a homogeneous isolated singularity, or it is a hyperplane arrangement, or it is a semi-invariant on a spherical variety. We give several immediate applications to our results, including a positive answer to a question of Torelli assuming the hypersurface has log canonical singularities: 1/f lies in the intersection complex of the hypersurface of f if and only if -1 is a simple root of b_f(s).

math.AG↗

arXiv2024

Introducing MeMo: A Multimodal Dataset for Memory Modelling in Multiparty Conversations

Conversational memory is the process by which humans encode, retain and retrieve verbal, non-verbal and contextual information from a conversation. Since human memory is selective, differing recollections of the same events can lead to misunderstandings and misalignments within a group. Yet, conversational facilitation systems, aimed at advancing the quality of group interactions, usually focus on tracking users' states within an individual session, ignoring what remains in each participant's memory after the interaction. Understanding conversational memory can be used as a source of information on the long-term development of social connections within a group. This paper introduces the MeMo corpus, the first conversational dataset annotated with participants' memory retention reports, aimed at facilitating computational modelling of human conversational memory. The MeMo corpus includes 31 hours of small-group discussions on Covid-19, repeated 3 times over the term of 2 weeks. It integrates validated behavioural and perceptual measures, audio, video, and multimodal annotations, offering a valuable resource for studying and modelling conversational memory and group dynamics. By introducing the MeMo corpus, analysing its validity, and demonstrating its usefulness for future research, this paper aims to pave the way for future research in conversational memory modelling for intelligent system development.

cs.CL↗

arXiv2020

Temporal Smoothing for 3D Human Pose Estimation and Localization for Occluded People

In multi-person pose estimation actors can be heavily occluded, even become fully invisible behind another person. While temporal methods can still predict a reasonable estimation for a temporarily disappeared pose using past and future frames, they exhibit large errors nevertheless. We present an energy minimization approach to generate smooth, valid trajectories in time, bridging gaps in visibility. We show that it is better than other interpolation based approaches and achieves state of the art results. In addition, we present the synthetic MuCo-Temp dataset, a temporal extension of the MuCo-3DHP dataset. Our code is made publicly available.

cs.CV↗

arXiv2020

Multi-Person Absolute 3D Human Pose Estimation with Weak Depth Supervision

In 3D human pose estimation one of the biggest problems is the lack of large, diverse datasets. This is especially true for multi-person 3D pose estimation, where, to our knowledge, there are only machine generated annotations available for training. To mitigate this issue, we introduce a network that can be trained with additional RGB-D images in a weakly supervised fashion. Due to the existence of cheap sensors, videos with depth maps are widely available, and our method can exploit a large, unannotated dataset. Our algorithm is a monocular, multi-person, absolute pose estimator. We evaluate the algorithm on several benchmarks, showing a consistent improvement in error rates. Also, our model achieves state-of-the-art results on the MuPoTS-3D dataset by a considerable margin.

cs.CV↗

arXiv2013

Emotional Expression Classification using Time-Series Kernels

Estimation of facial expressions, as spatio-temporal processes, can take advantage of kernel methods if one considers facial landmark positions and their motion in 3D space. We applied support vector classification with kernels derived from dynamic time-warping similarity measures. We achieved over 99% accuracy - measured by area under ROC curve - using only the 'motion pattern' of the PCA compressed representation of the marker point vector, the so-called shape parameters. Beyond the classification of full motion patterns, several expressions were recognized with over 90% accuracy in as few as 5-6 frames from their onset, about 200 milliseconds.

cs.CV↗

arXiv2013

The FuturICT Education Accelerator

Education is a major force for economic and social wellbeing. Despite high aspirations, education at all levels can be expensive and ineffective. Three Grand Challenges are identified: (1) enable people to learn orders of magnitude more effectively, (2) enable people to learn at orders of magnitude less cost, and (3) demonstrate success by exemplary interdisciplinary education in complex systems science. A ten year `man-on-the-moon' project is proposed in which FuturICT's unique combination of Complexity, Social and Computing Sciences could provide an urgently needed transdisciplinary language for making sense of educational systems. In close dialogue with educational theory and practice, and grounded in the emerging data science and learning analytics paradigms, this will translate into practical tools (both analytical and computational) for researchers, practitioners and leaders; generative principles for resilient educational ecosystems; and innovation for radically scalable, yet personalised, learner engagement and assessment. The proposed {\em Education Accelerator} will serve as a `wind tunnel' for testing these ideas in the context of real educational programmes, with an international virtual campus delivering complex systems education exploiting the new understanding of complex, social, computationally enhanced organisational structure developed within FuturICT.

physics.ed-ph↗

arXiv2012

Distributed High Dimensional Information Theoretical Image Registration via Random Projections

Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in high dimensions. On the other hand, consistent estimation from pairwise distances of the sample points is possible, which suits random projection (RP) based low dimensional embeddings. We adapt the RP technique to this task by means of a simple ensemble method. To the best of our knowledge, this is the first distributed, RP based information theoretical image registration approach. The efficiency of the method is demonstrated through numerical examples.

cs.IT↗

arXiv2012

Automated Word Puzzle Generation via Topic Dictionaries

We propose a general method for automated word puzzle generation. Contrary to previous approaches in this novel field, the presented method does not rely on highly structured datasets obtained with serious human annotation effort: it only needs an unstructured and unannotated corpus (i.e., document collection) as input. The method builds upon two additional pillars: (i) a topic model, which induces a topic dictionary from the input corpus (examples include e.g., latent semantic analysis, group-structured dictionaries or latent Dirichlet allocation), and (ii) a semantic similarity measure of word pairs. Our method can (i) generate automatically a large number of proper word puzzles of different types, including the odd one out, choose the related word and separate the topics puzzle. (ii) It can easily create domain-specific puzzles by replacing the corpus component. (iii) It is also capable of automatically generating puzzles with parameterizable levels of difficulty suitable for, e.g., beginners or intermediate learners.

cs.CL↗

arXiv2012

Collaborative Filtering via Group-Structured Dictionary Learning

Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based recommender systems. Our extensive numerical experiments demonstrate that the presented technique outperforms its state-of-the-art competitors and has several advantages over approaches that do not put structured constraints on the dictionary elements.

math.OC↗

arXiv2011

Decision Making Agent Searching for Markov Models in Near-Deterministic World

Reinforcement learning has solid foundations, but becomes inefficient in partially observed (non-Markovian) environments. Thus, a learning agent -born with a representation and a policy- might wish to investigate to what extent the Markov property holds. We propose a learning architecture that utilizes combinatorial policy optimization to overcome non-Markovity and to develop efficient behaviors, which are easy to inherit, tests the Markov property of the behavioral states, and corrects against non-Markovity by running a deterministic factored Finite State Model, which can be learned. We illustrate the properties of architecture in the near deterministic Ms. Pac-Man game. We analyze the architecture from the point of view of evolutionary, individual, and social learning.

cs.AI↗

arXiv2009

Optimistic Initialization and Greediness Lead to Polynomial Time Learning in Factored MDPs - Extended Version

In this paper we propose an algorithm for polynomial-time reinforcement learning in factored Markov decision processes (FMDPs). The factored optimistic initial model (FOIM) algorithm, maintains an empirical model of the FMDP in a conventional way, and always follows a greedy policy with respect to its model. The only trick of the algorithm is that the model is initialized optimistically. We prove that with suitable initialization (i) FOIM converges to the fixed point of approximate value iteration (AVI); (ii) the number of steps when the agent makes non-near-optimal decisions (with respect to the solution of AVI) is polynomial in all relevant quantities; (iii) the per-step costs of the algorithm are also polynomial. To our best knowledge, FOIM is the first algorithm with these properties. This extended version contains the rigorous proofs of the main theorem. A version of this paper appeared in ICML'09.

cs.AI↗

arXiv2008

Factored Value Iteration Converges

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.

cs.AI↗

arXiv2008

Model of the hippocampal formation explains the coexistence of grid cells and place cells

In this paper we explain the strikingly regular activity of the 'grid' cells in rodent dorsal medial entorhinal cortex (dMEC) and the spatially localized activity of the hippocampal place cells in CA3 and CA1 by assuming that the hippocampal region is constructed to support an internal dynamical model of the sensory information. The functioning of the different areas of the hippocampal-entorhinal loop and their interaction are derived from a set of information theoretical principles. We demonstrate through simple transformations of the stimulus representations that the double form of space representation (i.e. place field and regular grid tiling) can be seen as a computational 'by-product' of the circuit. In contrast to other theoretical or computational models we can also explain how place and grid activity may emerge at the respective areas simultaneously. In accord with recent views, our results point toward a close relation between the formation of episodic memory and spatial navigation.

q-bio.NC↗

arXiv2008

Online variants of the cross-entropy method

The cross-entropy method is a simple but efficient method for global optimization. In this paper we provide two online variants of the basic CEM, together with a proof of convergence.

cs.LG↗

arXiv2008

D-optimal Bayesian Interrogation for Parameter and Noise Identification of Recurrent Neural Networks

We introduce a novel online Bayesian method for the identification of a family of noisy recurrent neural networks (RNNs). We develop Bayesian active learning technique in order to optimize the interrogating stimuli given past experiences. In particular, we consider the unknown parameters as stochastic variables and use the D-optimality principle, also known as `\emph{infomax method}', to choose optimal stimuli. We apply a greedy technique to maximize the information gain concerning network parameters at each time step. We also derive the D-optimal estimation of the additive noise that perturbs the dynamical system of the RNN. Our analytical results are approximation-free. The analytic derivation gives rise to attractive quadratic update rules.

cs.NE↗

arXiv2007

Undercomplete Blind Subspace Deconvolution via Linear Prediction

We present a novel solution technique for the blind subspace deconvolution (BSSD) problem, where temporal convolution of multidimensional hidden independent components is observed and the task is to uncover the hidden components using the observation only. We carry out this task for the undercomplete case (uBSSD): we reduce the original uBSSD task via linear prediction to independent subspace analysis (ISA), which we can solve. As it has been shown recently, applying temporal concatenation can also reduce uBSSD to ISA, but the associated ISA problem can easily become `high dimensional' [1]. The new reduction method circumvents this dimensionality problem. We perform detailed studies on the efficiency of the proposed technique by means of numerical simulations. We have found several advantages: our method can achieve high quality estimations for smaller number of samples and it can cope with deeper temporal convolutions.

stat.ME↗

arXiv2007

Undercomplete Blind Subspace Deconvolution

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high dimensional' ISA problem can be handled by a recent technique called joint f-decorrelation (JFD). Similar decorrelation methods have been used previously for kernel independent component analysis (kernel-ICA). More precisely, the kernel canonical correlation (KCCA) technique is a member of this family, and, as is shown in this paper, the kernel generalized variance (KGV) method can also be seen as a decorrelation method in the feature space. These kernel based algorithms will be adapted to the ISA task. In the numerical examples, we (i) examine how efficiently the emerging higher dimensional ISA tasks can be tackled, and (ii) explore the working and advantages of the derived kernel-ISA methods.

math.ST↗

arXiv2007

Independent Process Analysis without A Priori Dimensional Information

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As a particular application, we search for subspaces of facial components.

math.ST↗