The unbiased estimation of the fraction of variance explained by a model

Pospisil, Dean A.; Bair, Wyeth

doi:10.1101/2020.10.30.361253

Cited by 4 publications

(9 citation statements)

References 16 publications

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“…For this purpose we show the consistency of our main results (Fig. 5 in the paper), by comparing the fraction oracle to another measure, the fraction of variance of the expected response (r 2 ER ) (Pospisil & Bair, 2020). The calculation of the r 2 ER assumes that the variance over image repeats across unique images is constant.…”

Section: Consistency Across Other Performance Measuresmentioning

confidence: 55%

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Generalization in data-driven models of primary visual cortex

Lurz

Bashiri

Willeke

et al. 2020

Preprint

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Deep neural networks (DNN) have set new standards at predicting responses of neural populations to visual input. Most such DNNs consist of a convolutional network (core) shared across all neurons which learns a representation of neural computation in visual cortex and a neuron-specific readout that linearly combines the relevant features in this representation. The goal of this paper is to test whether such a representation is indeed generally characteristic for visual cortex, i.e. generalizes between animals of a species, and what factors contribute to obtaining such a generalizing core. To push all non-linear computations into the core where the generalizing cortical features should be learned, we devise a novel readout that reduces the number of parameters per neuron in the readout by up to two orders of magnitude compared to the previous state-of-the-art. It does so by taking advantage of retinotopy and learns a Gaussian distribution over the neuron’s receptive field position. With this new readout we train our network on neural responses from mouse primary visual cortex (V1) and obtain a gain in performance of 7% compared to the previous state-of-the-art network. We then investigate whether the convolutional core indeed captures general cortical features by using the core in transfer learning to a different animal. When transferring a core trained on thousands of neurons from various animals and scans we exceed the performance of training directly on that animal by 12%, and outperform a commonly used VGG16 core pre-trained on imagenet by 33%. In addition, transfer learning with our data-driven core is more data-efficient than direct training, achieving the same performance with only 40% of the data. Our model with its novel readout thus sets a new state-of-the-art for neural response prediction in mouse visual cortex from natural images, generalizes between animals, and captures better characteristic cortical features than current task-driven pre-training approaches such as VGG16.

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Section: Consistency Across Other Performance Measuresmentioning

confidence: 55%

“…Furthermore, the authors recommend that the signal-to-noise ratio of the data must be above a certain threshold (0.1 for data with 100 images and 10 repeats each, as in our case; see Fig. 14 in Pospisil & Bair (2020)). Our data meets this criterion (see Fig.…”

Section: Consistency Across Other Performance Measuresmentioning

confidence: 95%

Generalization in data-driven models of primary visual cortex

Lurz

Bashiri

Willeke

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…2). The fraction of variance explained (Pospisil & Bair, 2020) was was 0.35 (.314±0.002 for individual models), which is Fig. 1.…”

Section: Resultsmentioning

confidence: 78%

“…Secondly, we computed the correlation of the predicted responses with the average responses across repeats and refer to it here as correlation to average. We also computed the fraction of variance explained, using proposed by (Pospisil & Bair, 2020), which provides an unbiased estimate of the variance explained based on the expected neuronal response across image repetitions. However, our model computed different predictions for each repetition of a given test set image, because we also fed the behavioral parameters of each trial into the model.…”

Section: Methodsmentioning

confidence: 99%

Behavioral state tunes mouse vision to ethological features through pupil dilation

Franke

Willeke

Ponder

et al. 2021

Preprint

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Across animal species, sensory processing dynamically adapts to behavioral context. In the mammalian visual system, sensory neural responses and behavioral performance increase during an active behavioral state characterized by locomotion activity and pupil dilation, whereas preferred stimuli of individual neurons typically remain unchanged. Here, we address how behavioral states modulate stimulus selectivity in the context of colored natural scenes using a combination of large-scale population imaging, behavior, pharmacology, and deep neural network modeling. In visual cortex of awake mice, we identified a consistent shift of individual neuron color preferences towards ultraviolet stimuli during active behavioral periods that was particularly pronounced in the upper visual field. We found that the spectral shift in neural tuning is mediated by pupil dilation, resulting in a dynamic switch from rod- to cone-driven visual responses for constant ambient light levels. We further showed that this shift selectively enhances the discriminability of ultraviolet objects and facilitates the detection of ethological stimuli, such as aerial predators against the ultraviolet background of the twilight sky. Our results suggest a novel functional role for pupil dilation during active behavioral states as a bottom-up mechanism that, together with top-down neuromodulatory mechanisms, dynamically tunes visual representations to different behavioral demands.

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“…The form of the most common correction, given by Spearman (1904), multiplies the correlation coefficient by the inverse of its estimated attenuation. Here we follow an approach developed in the neuroscience literature (Pospisil and Bair, 2020;Haefner and Cumming, 2008;Sahani and Linden, 2003) that removes the bias from the sample covariance and variance separately then forms their ratio for the corrected estimate. We call our estimatorr 2 ER as it estimates the fraction of variance explained between the expected responses (r 2 ER ) of the neurons or equivalently their tuning curves.…”

Section: Introductionmentioning

confidence: 99%

The unbiased estimation ofr²between two sets of noisy neural responses

Pospisil¹,

Bair²

2021

Preprint

Self Cite

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The Pearson correlation coefficient squared, r2, is often used in the analysis of neural data to estimate the relationship between neural tuning curves. Yet this metric is biased by trial-to-trial variability: as trial-to-trial variability increases, measured correlation decreases. Major lines of research are confounded by this bias, including the study of invariance of neural tuning across conditions and the similarity of tuning across neurons. To address this, we extend the estimator, r̂2ER, developed for estimating model-to-neuron correlation to the neuron-to-neuron case. We compare the estimator to a prior method developed by Spearman, commonly used in other fields but widely overlooked in neuroscience, and find that our method has less bias. We then apply our estimator to the study of two forms of invariance and demonstrate how it avoids drastic confounds introduced by trial-to-trial variability.

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The unbiased estimation of the fraction of variance explained by a model

Cited by 4 publications

References 16 publications

Generalization in data-driven models of primary visual cortex

Generalization in data-driven models of primary visual cortex

Behavioral state tunes mouse vision to ethological features through pupil dilation

The unbiased estimation ofr²between two sets of noisy neural responses

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The unbiased estimation of the fraction of variance explained by a model

Cited by 4 publications

References 16 publications

Generalization in data-driven models of primary visual cortex

Generalization in data-driven models of primary visual cortex

Behavioral state tunes mouse vision to ethological features through pupil dilation

The unbiased estimation ofr2between two sets of noisy neural responses

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The unbiased estimation ofr²between two sets of noisy neural responses