Model-Free Estimation of Tuning Curves and Their Attentional Modulation, Based on Sparse and Noisy Data
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{"title"=>"Model-free estimation of tuning curves and their attentional modulation, based on sparse and noisy data", "type"=>"journal", "authors"=>[{"first_name"=>"Markus", "last_name"=>"Helmer", "scopus_author_id"=>"57117702300"}, {"first_name"=>"Vladislav", "last_name"=>"Kozyrev", "scopus_author_id"=>"7006462207"}, {"first_name"=>"Valeska", "last_name"=>"Stephan", "scopus_author_id"=>"35312544700"}, {"first_name"=>"Stefan", "last_name"=>"Treue", "scopus_author_id"=>"6701706021"}, {"first_name"=>"Theo", "last_name"=>"Geisel", "scopus_author_id"=>"7006784868"}, {"first_name"=>"Demian", "last_name"=>"Battaglia", "scopus_author_id"=>"7006321888"}], "year"=>2016, "source"=>"PLoS ONE", "identifiers"=>{"pmid"=>"26785378", "sgr"=>"84958191443", "doi"=>"10.1371/journal.pone.0146500", "scopus"=>"2-s2.0-84958191443", "pui"=>"608240578", "issn"=>"19326203"}, "id"=>"60d12d25-23a5-35e7-af2d-e7a070e1320a", "abstract"=>"Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.", "link"=>"http://www.mendeley.com/research/modelfree-estimation-tuning-curves-attentional-modulation-based-sparse-noisy-data-3", "reader_count"=>12, "reader_count_by_academic_status"=>{"Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>3, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>3, "Other"=>1, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Agricultural and Biological Sciences"=>3, "Neuroscience"=>4, "Physics and Astronomy"=>1, "Psychology"=>2, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Neuroscience"=>{"Neuroscience"=>4}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Psychology"=>{"Psychology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>3}, "Computer Science"=>{"Computer Science"=>1}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"United States"=>2, "Chile"=>1, "Germany"=>3}, "group_count"=>2}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2629345"], "description"=>"<p>Direction selective responses of MT cells were measured using different direction combinations of stimuli and different attentional conditions. The stimuli in the receptive field (RF) of the recorded cell were either two random dot patterns (RDP) moving in directions 120° apart and placed in spatially separated (panels A–B) or overlapping (panels C–D) apertures or just one single (unidirectional) RDP (panel E). A cue instructed the monkey to attend to either: a luminance change of the fixation point (FP), in the attend-fix condition (afix, panels A and C) and single stimulus (uni, panel E) conditions; or to changes of the direction or velocity of the cued RDP (orange) in the RF, in the attend-in conditions (ain, panels B and D). The transparent uni condition was taken to be the cue-period of the ain condition (panel D). F: Example of a “well-behaved” tuning curve from the spatially separated paradigm in the afix condition. Gray circles denote trial-averaged firing rates and error bars their standard deviation. A sum-of-two-gaussians fit is also shown (brown). The stimulus directions are aligned for each cell, so that the attended direction corresponds to the preferred direction in the uni condition at 240° (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#sec011\" target=\"_blank\">Materials and Methods</a> for details).</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638917, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Attentional_experiments_/1638917", "title"=>"Attentional experiments.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629347"], "description"=>"<p>A: typical example of tuning curve from the spatially-separated afix condition (compare with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#pone.0146500.g001\" target=\"_blank\">Fig 1F</a>). The shape of the curve—including the position of the two peaks that should be elicited by the composite RDP stimulus—cannot reliably be inferred due to large error bars (std.). B: Histogram of estimated firing rate standard deviations (expressed in relative units, as ratios between std. and a matching mean), obtained by lumping together all stimulus directions and attentional conditions, for the spatially separated (left) and the transparent (right) paradigms. Both these histograms are strongly right-skewed, denoting the existence of cells with highly variable responses to certain stimuli.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638919, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Many_tuning_curves_are_not_8220_well_behaved_8221_/1638919", "title"=>"Many tuning curves are not “well-behaved”.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629349"], "description"=>"<p><b>A)</b> Eight model functions were fitted to an example tuning curve (gray error bars denote std.) from the transparent afix condition. Due to the tuning curve’s large error bars all models provided good fits even though they clearly differ. <b>B)</b> According to a goodness-of-fit score (see main text) all eight models provided good fits for almost all cells, independent of experimental condition and paradigm. <b>C)</b> The Akaike Information Criterion AIC was thus employed to select the best (ΔAIC = 0) or at least close to best (ΔAIC≤1) model for each cell. The fraction of cells for which each model constitutes the respective best or almost best model is illustrated with full and light bars. No model was chosen for all cells, still the most widely selected model was the fourth order Fourier series (<i>F</i>4). Both of these facts mirror the high heterogeneity in the data that is hard to capture in a single tuning curve shape. <b>Color code</b> red: 2nd order Fourier (F2); blue: 3rd order Fourier (F3); green: 4th order Fourier (F4); violet: symmetric Beta (s<i>β</i>); orange—von Mises (vM); yellow: wrapped Cauchy (wC); brown: wrapped Gaussian (wG); pink: wrapped generalized bell-shaped membership function (wB).</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638921, "categories"=>["Uncategorised"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Many_models_are_consistent_with_the_data_/1638921", "title"=>"Many models are consistent with the data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629351"], "description"=>"<p><b>A)</b> We describe all tuning curve properties of interest by algorithmically extracted features, as opposed to model parameters. The panel gives pseudocode for three selected features, illustrated also in panels B,C in corresponding colors. <b>B</b>) Feature extraction algorithms take as input only the sampled fitted tuning curve. Features are thus defined independent of a model function, allowing for their comparison between models. Furthermore, all aspects of tuning curves can be described by suitably chosen features such as Maximum<sup>left</sup> (dark red), InnerMinimum (orange), Maximum<sup>right</sup> (blue), (occuring at positions MaximumAngle<sup>left</sup>, InnerMinimumAngle and MaximumAngle<sup>right</sup>, respectively), InnerWidth<sup>left</sup> (pink), InnerWidth<sup>right</sup> (green). <b>C)</b> Due to their algorithmic nature feature extraction rules can equally well be applied directly to the coarse measured trial-averaged tuning curve. Thereby, tuning curve properties can be described and analyzed without referring to the fit.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638923, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g004", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Alternative_to_fitting_algorithmic_features_/1638923", "title"=>"Alternative to fitting: algorithmic features.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:57:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629352"], "description"=>"<p><b>A)</b> Nine features, measuring aspects of firing rate (first column), width (second column) and global shape (third column) in all three conditions were calculated for each cell on the basis of eight fitted models (model abbreviations are as in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#pone.0146500.g003\" target=\"_blank\">Fig 3</a>) and the “best model” (according to the ΔAIC = 0 criterion, see main text; abbreviated “bM”). Red (blue) indicates a statistically significant (not sig.) difference between two models’ values of that feature. Results from the spatially separated and transparent paradigm are plotted below and above the diagonal, respectively. The panels indicate that, in general, models disagree on the value of a feature, and, in particular, might contradict the optimal (bM) model. <b>B)</b> Histograms count for all feature pairs (depending on their category “sp.sep vs trans”, “sp.sep vs sp.sep” or “trans vs trans”) the number of model functions that find a significant difference (“effect”) between the pair. While mostly all models agree (counts 0 and 9) there are also numerous cases in which the presence of an effect depends on the chosen model.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638924, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g005", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_found_in_the_data_depend_on_model_/1638924", "title"=>"Effects found in the data depend on model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:57:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629353"], "description"=>"<p><b>A)</b> Layout is similar to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#pone.0146500.g005\" target=\"_blank\">Fig 5B</a>. Each bar from there was split into two, depending on if a considered feature pair was judged significantly different (blue) or not (green) when evaluated with the direct method. The panel illustrates a strong tendency to find a significant effect with either both the direct method and all nine models, or with neither the direct method and none of the models. <b>B)</b><i>z</i>-scored quantitative differences between direct and fitted method’s feature values is less than one standard deviation for almost all features independent of the model indicating a considerable quantitative agreement between the methods. Solid lines in violines mark 2.5%, 50% and 97.5% quantiles. Color code and model abbreviations are as in Figs <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#pone.0146500.g003\" target=\"_blank\">3</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146500#pone.0146500.g005\" target=\"_blank\">5</a>.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638925, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g006", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Direct_method_yields_very_similar_results_as_fits_/1638925", "title"=>"Direct method yields very similar results as fits.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629354"], "description"=>"<p>Scatter plots of various features in the afix versus the ain condition. Orange error ellipses are centered on the mean feature values with half-axes corresponding to eigenvalues and -vectors of the feature-pair’s covariance matrix. Some outliers were omitted for better visualization. The indicated <i>p</i>-value in each panel corresponds to a Kruskal-Wallis test. <b>A)</b> Attention decreased (increased) the left peak—as measured by the feature normalizedPeakToPeak<sup>left</sup>—in the spatially separated (transparent) paradigm. <b>B)</b> Attention increased the right peak in both paradigms according to the feature normalizedPeakToPeak<sup>right</sup>. <b>C)</b> Attention significantly increased the difference between left and right peak’s inner width—ΔInnerWidth—only for the spatially separated paradigm. Size of circles in panel C illustrates density of points at each particular coordinate (note that values of ΔInnerWidth from the direct method are quantized in steps of 30°due to the design of experimentally used stimuli). Altogether panels indicate that attention asymetrically expanded the right at the expense of the left peak for the spatially separated paradigm, but increased both peaks similarly for the transparent paradigm.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638926, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g007", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_of_attention_on_tuning_curves_/1638926", "title"=>"Effects of attention on tuning curves.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629355"], "description"=>"<p><b>A)</b> Each dot in this cartoon (not based on measured data) represents the observed spike count in one trial. For a given stimulus, spike count distributions can differ between experimental conditions either significantly (e. g. at 60°) or not (e. g. at 240°). <b>B)</b> Distribution of the proportion of cells with a significant difference between conditions for a given number of stimuli (maximum 12). The green histograms represent the two conditions where a second stimulus was added and pink histograms the conditions where attention was switched. <b>C-F)</b> Histograms show the stimulus-dependent fraction of cells with a non-significant response modulation (blue), a significant response enhancement (green) or response suppression (pink). The dotted and orange arrows along the <i>x</i>-axes in E and F indicate the RDP direction not present in the uni condition and the attended RDP in ain condition, respectively. Across the population a second stimulus tended to increase firing rates around 120°(C,D) and to decrease them around 240°. Attention asymmetrically affected the left and right peak in the spatially separated paradigm (E) whereas it symmetrically increased both peaks for the transparent paradigm (F). These stimulus-specific changes were compatible with the results of the direct method discussed in the text.</p>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638927, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146500.g008", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_of_adding_a_second_stimulus_or_attention_to_the_receptive_field_/1638927", "title"=>"Effects of adding a second stimulus or attention to the receptive field.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 12:37:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/2629366", "https://ndownloader.figshare.com/files/2629367", "https://ndownloader.figshare.com/files/2629368", "https://ndownloader.figshare.com/files/2629369", "https://ndownloader.figshare.com/files/2629370", "https://ndownloader.figshare.com/files/2629371", "https://ndownloader.figshare.com/files/2629372", "https://ndownloader.figshare.com/files/2629373", "https://ndownloader.figshare.com/files/2629374", "https://ndownloader.figshare.com/files/2629375", "https://ndownloader.figshare.com/files/2629376", "https://ndownloader.figshare.com/files/2629377", "https://ndownloader.figshare.com/files/2629378", "https://ndownloader.figshare.com/files/2629379", "https://ndownloader.figshare.com/files/2629380", "https://ndownloader.figshare.com/files/2629381"], "description"=>"<div><p>Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.</p></div>", "links"=>[], "tags"=>["attentional gain modulations", "attentional modulation patterns", "approach", "mt", "Noisy Data Tuning curves", "response", "model selection"], "article_id"=>1638932, "categories"=>["Biological Sciences"], "users"=>["Markus Helmer", "Vladislav Kozyrev", "Valeska Stephan", "Stefan Treue", "Theo Geisel", "Demian Battaglia"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0146500.s001", "https://dx.doi.org/10.1371/journal.pone.0146500.s002", "https://dx.doi.org/10.1371/journal.pone.0146500.s003", "https://dx.doi.org/10.1371/journal.pone.0146500.s004", "https://dx.doi.org/10.1371/journal.pone.0146500.s005", "https://dx.doi.org/10.1371/journal.pone.0146500.s006", "https://dx.doi.org/10.1371/journal.pone.0146500.s007", "https://dx.doi.org/10.1371/journal.pone.0146500.s008", "https://dx.doi.org/10.1371/journal.pone.0146500.s009", "https://dx.doi.org/10.1371/journal.pone.0146500.s010", "https://dx.doi.org/10.1371/journal.pone.0146500.s011", "https://dx.doi.org/10.1371/journal.pone.0146500.s012", "https://dx.doi.org/10.1371/journal.pone.0146500.s013", "https://dx.doi.org/10.1371/journal.pone.0146500.s014", "https://dx.doi.org/10.1371/journal.pone.0146500.s015", "https://dx.doi.org/10.1371/journal.pone.0146500.s016"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_Free_Estimation_of_Tuning_Curves_and_Their_Attentional_Modulation_Based_on_Sparse_and_Noisy_Data_/1638932", "title"=>"Model-Free Estimation of Tuning Curves and Their Attentional Modulation, Based on Sparse and Noisy Data", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2016-01-28 12:37:39"}

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{"start_date"=>"2016-01-01T00:00:00Z", "end_date"=>"2016-12-31T00:00:00Z", "subject_areas"=>[]}
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