1,721,004 research outputs found
Likelihood Methods for Point Processes with Refractoriness
No full textLikelihood-based encoding models founded on point processes have received significant attention in the literature because of their ability to reveal the information encoded by spiking neural populations. We propose an approximation to the likelihood of a point-process model of neurons that holds under assumptions about the continuous time process that are physiologically reasonable for neural spike trains: the presence of a refractory period, the predictability of the conditional intensity function, and its integrability. These are properties that apply to a large class of point processes arising in applications other than neuroscience. The proposed approach has several advantages over conventional ones. In particular, one can use standard fitting procedures for generalized linear models based on iteratively reweighted least squares while improving the accuracy of the approximation to the likelihood and reducing bias in the estimation of the parameters of the underlying continuous-time model. As a result, the proposed approach can use a larger bin size to achieve the same accuracy as conventional approaches would with a smaller bin size. This is particularly important when analyzing neural data with high mean and instantaneous firing rates. We demonstrate these claims on simulated and real neural spiking activity. By allowing a substantive increase in the required bin size, our algorithm has the potential to lower the barrier to the use of point-process methods in an increasing number of applications.National Institutes of Health (U.S.) (Grant R01-HL084502)National Institutes of Health (U.S.) (Grant DP1-OD003646
Exact and stable recovery of sequences of signals with sparse increments via differential ℓ1-minimization
Full text linkWe consider the problem of recovering a sequence of vectors, (Xk)[K over k=0], for which the increments X[subscript k] - X[subscript k-1] are S[subscript k]-sparse (with S[subscript k] typically smaller than S[subscript 1]), based on linear measurements (Y[subscript k] = A[subscript k]X[subscript k] + e[subscript k)[superscript K over k=1, where A[subscript k] and e[subscript k] denote the measurement matrix and noise, respectively. Assuming each A[subscript k] obeys the restricted isometry property (RIP) of a certain order--depending only on S[subscript k]--we show that in the absence of noise a convex program, which minimizes the weighted sum of the ℓ [subscript 1]-norm of successive differences subject to the linear measurement constraints, recovers the sequence (Xk)[K over k=1] exactly. This is an interesting result because this convex program is equivalent to a standard compressive sensing problem with a highly-structured aggregate measurement matrix which does not satisfy the RIP requirements in the standard sense, and yet we can achieve exact recovery. In the presence of bounded noise, we propose a quadratically-constrained convex program for recovery and derive bounds on the reconstruction error of the sequence. We supplement our theoretical analysis with simulations and an application to real video data. These further support the validity of the proposed approach for acquisition and recovery of signals with time-varying sparsity
Missing mass approximations for the partition function of stimulus driven Ising models
No full textIsing models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN[subscript pat]) where is L the data length, N the number of neurons and N[subscript pat] the number of unique patterns in the data, contrasting with the O(L2[superscript N]) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.National Institutes of Health (U.S.) (Grant K25 NS052422-02
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Group Symmetries in Diffusion Models: Formulation, Generalization, and Enforcement
No full textGroup symmetries are fundamental structures in many real-world datasets, and lever- aging them is crucial for building robust and data-efficient machine learning models. Diffusion models have achieved state-of-the-art performance in generative tasks but typically rely on standard neural network architectures for score estimation. This thesis investigates whether such standard configurations enable diffusion models to implicitly learn and generalize underlying data symmetries purely from examples, particularly when data is partially observed. Drawing motivation from Neural Tangent Kernel (NTK) theory, which suggests limitations in the ability of standard supervised networks to generalize symmetries beyond local data structure, we hypothesize and empirically demonstrate that score networks in diffusion models exhibit similar constraints. Using a 2D toy dataset with inherent SO(2) rotational symmetry, we show a consistent failure of standard models trained on incomplete data (interpolation and extrapolation settings) to generalize symmetry, exhibiting significant score field distortions in unobserved regions. To address this limitation, we propose and evaluate a novel per-timestep symmetry loss that regularizes the denoising process to encourage approximate equivariance. Empirical results on both the toy dataset and higher-dimensional MNIST data confirm that this loss significantly enhances symmetry generalization even in standard architectures, yielding geometrically consistent results comparable to extensive data augmentation. This work highlights a critical limitation in standard diffusion models and underscores the importance of incorporating explicit geometric biases, via architecture or regularization, for reliable generative modeling on structured data.Computer Scienc
Algorithms for the analysis of ensemble neural spiking activity using simultaneous-event multivariate point-process models
Full text linkUnderstanding how ensembles of neurons represent and transmit information in the patterns of their joint spiking activity is a fundamental question in computational neuroscience. At present, analyses of spiking activity from neuronal ensembles are limited because multivariate point process (MPP) models cannot represent simultaneous occurrences of spike events at an arbitrarily small time resolution. Solo recently reported a simultaneous-event multivariate point process (SEMPP) model to correct this key limitation. In this paper, we show how Solo's discrete-time formulation of the SEMPP model can be efficiently fit to ensemble neural spiking activity using a multinomial generalized linear model (mGLM). Unlike existing approximate procedures for fitting the discrete-time SEMPP model, the mGLM is an exact algorithm. The MPP time-rescaling theorem can be used to assess model goodness-of-fit. We also derive a new marked point-process (MkPP) representation of the SEMPP model that leads to new thinning and time-rescaling algorithms for simulating an SEMPP stochastic process. These algorithms are much simpler than multivariate extensions of algorithms for simulating a univariate point process, and could not be arrived at without the MkPP representation. We illustrate the versatility of the SEMPP model by analyzing neural spiking activity from pairs of simultaneously-recorded rat thalamic neurons stimulated by periodic whisker deflections, and by simulating SEMPP data. In the data analysis example, the SEMPP model demonstrates that whisker motion significantly modulates simultaneous spiking activity at the 1 ms time scale and that the stimulus effect is more than one order of magnitude greater for simultaneous activity compared with non-simultaneous activity. Together, the mGLM, the MPP time-rescaling theorem and the MkPP representation of the SEMPP model offer a theoretically sound, practical tool for measuring joint spiking propensity in a neuronal ensemble.Version of Recor
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Estimation of Hearing Aid Head Related Transfer Functions using Anthropometric Features
No full textVirtual reality is emerging as an ecologically valid environment for auditory rehabilitation and diagnostics. Creating an auditory environment that accurately simulates a user’s experience requires accurate knowledge of their Head-Related Transfer Functions (HRTFs). However, these vary due to differences in physical features and can lead to the incorrect simulation of sound if the HRTFs used are too dissimilar to a listener’s. This issue is exacerbated by the use of a hearing device as sound is transmitted to the eardrum from a microphone located elsewhere on the ear, changing the path of sound and consequently the HRTFs. This project presents a method of identifying a suitable set of HRTFs from a dataset, performing better than chance and leads to a localisation error 1.2◦greater than a subject using their HRTFs
Robust spectrotemporal decomposition by iteratively reweighted least squares
Full text linkClassical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series. This universally accepted approach fails to exploit the temporal continuity in the data and is not well-suited for signals with highly structured time–frequency representations. For a time series whose time-varying mean is the superposition of a small number of oscillatory components, we formulate nonparametric batch spectral analysis as a Bayesian estimation problem. We introduce prior distributions on the time–frequency plane that yield maximum a posteriori (MAP) spectral estimates that are continuous in time yet sparse in frequency. Our spectral decomposition procedure, termed spectrotemporal pursuit, can be efficiently computed using an iteratively reweighted least-squares algorithm and scales well with typical data lengths. We show that spectrotemporal pursuit works by applying to the time series a set of data-derived filters. Using a link between Gaussian mixture models, ℓ[subscript 1] minimization, and the expectation–maximization algorithm, we prove that spectrotemporal pursuit converges to the global MAP estimate. We illustrate our technique on simulated and real human EEG data as well as on human neural spiking activity recorded during loss of consciousness induced by the anesthetic propofol. For the EEG data, our technique yields significantly denoised spectral estimates that have significantly higher time and frequency resolution than multitaper spectral estimates. For the neural spiking data, we obtain a new spectral representation of neuronal firing rates. Spectrotemporal pursuit offers a robust spectral decomposition framework that is a principled alternative to existing methods for decomposing time series into a small number of smooth oscillatory components.National Institutes of Health (U.S.) (Transformative Research Award GM 104948)National Institutes of Health (U.S.) (New Innovator Award R01-EB006385
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Leveraging Low-Dimensional Structure to Enable Spatial Transcriptomics
No full textInformation about biological phenotype can be gleaned from a variety of sources. We’ve made rapid progress in the last decade in more and more accurate measurements of one, central source: gene expression levels inside of cells. We’re now able to rapidly and cheaply sequence the content and abundance of RNA transcripts down to single-cell resolution. However, in the process we lose information regarding the spatial context of the cell: where in the tissue it originated from. Techniques have been developed in the last few years to remedy this problem, by incorporating spatial information into gene expression measurements. However, these techniques tend to be restricted to the lab of origin due to their high degree of technical complexity. We aim to alleviate this problem by using low-dimensional structure in gene expression profiles to use low-dimensional experimental measurements that are widely accessible to impute the full, high-dimensional spatial transcriptome
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Video Representation Learning via Actons
No full textIn this paper, we propose a novel method for dense video representation learning. Through our method, we are able to learn compressed frame representations known as “actons”. By extracting actons, we strike a middle ground between expressive but computationally de- manding frame-wise features and low information whole-video features. Our model consists of two-branch processing using a VQ-Codebook and a Transformer encoder trained on the Masked-Language Modeling protocol. In order to fit within the scope of this work, we extract small-scale datasets from TinyVIRAT and UCF101, both action recognition datasets, which we use to evaluate our methods. We find that our acton representations are far smaller than original video lengths, reaching compression ratios up to 18x, that are also more expressive than framewise features. We also find that fine-tuning using our representations achieves better test-set accuracy on action classification when compared to a C3D baseline
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