Decodanda

Decodanda (dog-latin for "to be decoded") is a Python package for decoding and geometrical analysis of neural activity.

Decodanda is designed to expose a user-friendly and flexible interface for population activity decoding, avoiding the most common pitfalls by a series of built-in best practices:

• Cross-validation is automatically implemented using a default or specified trial structure
• All analyses come with a built-in null model to test the significance of the data performance (notebook)
• Multi-sessions pooling to create pseudo-populations is supported out of the box (notebook)
• The individual contributions of multiple correlated experimental variables are isolated by cross-variable data balancing, avoding the confounding effects of correlated variables (notebook)

In addition, Decodanda exposes a series of functions to analyze the geometrical properties of neural code, such as the Cross-Condition Generalization Performance (CCGP, Bernardi et al. 2020), Parallelism Score, and more (notebook). Also see this class material on how to use decoding and CCGP to retrieve the representational geometry.

Please refer to the notebooks for some examples on

• single-variable decoding (with null model)
• multi-variable decoding (disentangling correlated variables)
• pseudo-population decoding (pooling neurons from multiple data sets)
• decoding in time
• CCGP and geometrical analysis

For a guided explanation of some of the best practices implemented by Decodanda, you can refer to my teaching material for the Advanced Theory Course in Neuroscience at Columbia University.

If you are interested in collaborating or contributing to the project, get in touch with me through this module or shoot me an old-fashioned email!.

Have fun, drink water, and decode safely!

Getting started

Install

---

Decodanda can be installed via pip:

pip install decodanda

Alternatively, to install Decodanda locally, run

python3 setup.py install

from the home folder of the package. It is recommended to use a virtual environment to manage packages and dependencies.

Documentation

Visit https://decodanda.readthedocs.io for the complete documentation.

Data structure

---

Decodanda works with datasets organized into Python dictionaries. For N recorded neurons and T trials (or time bins), the data dictionary must contain:

1. a TxN array, under the raster key

This is the set of features we use to decode. Can be continuous (e.g., calcium fluorescence) or discrete (e.g., spikes) values.

2. a Tx1 array specifying a trial number

This array will define the subdivisions for cross validation: trials (or time bins) that share the same trial value will always go together in either training or testing samples.

3. a Tx1 array for each variable we want to decode

Each value will be used as a label for the raster feature. Make sure these arrays are synchronized with the raster array.

A properly-formatted data set with two experimental variables (here, stimulus and action) would look like this:

data = {
    'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],   # <TxN array>, neural activations 
    'trial':  [0, 0, 0, ..., T],                       # <Tx1 array>, trial number
    'stimulus': [-1, -1, 1, ..., 1],                   # <Tx1 array>, binary labels for stimulus
    'action': [1, -1, 1, ..., -1],                     # <Tx1 array>, binary labels for action
}

Use cases

Decoding one variable from neural activity

---

(Notebook)

All decoding functions are implemented as methods of the Decodanda class. The constructor of this class takes two main objects:

• data: a single dictionary, or a list of dictionaries, containing the data to analyze. In the case of N neurons and T trials (or time bins), each data dictionary must contain:

  • the neural data:

    TxN array, under the raster key (you can specify a different one)

  • the values of the variables we want to decode

    Tx1 array per variable

  • the trial number (independent samples for cross validation):

    Tx1 array

• conditions: a dictionary specifying what variable(s) and what values we want to decode from the data.

For example, if we want to decode the variable stimulus, which takes values A, B from simultaneous recordings of N neurons x T trials we will have:

from decodanda import Decodanda

data = {
    'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],   # <TxN array>, neural activations 
    'stimulus': ['A', 'A', 'B', ..., 'B'],             # <Tx1 array>, labels
    'trial':  [1, 2, 3, ..., T],                       # <Tx1 array>, trial number
}

conditions = {
    'stimulus': ['A', 'B']
}

dec = Decodanda(
        data=data,
        conditions=conditions)

To perform the cross-validated decoding analysis for stimulus, call the decode() method

performances, null = dec.decode(
                        training_fraction=0.5,  # fraction of trials used for training
                        cross_validations=10,   # number of cross validation folds
                        nshuffles=20)           # number of null model iterations

which outputs

>>> performances
{'stimulus': 0.78}  # mean decoding performance over the cross_validations folds
>>> null
{'stimulus' [0.52, 0.49, 0.54 ... 0.49]}  # nshuffles (20) values

If plot=true is specified in decode(), the function will show the performance compared to the null model (with errorbars spanning 2 STDs) and a significance notation based on the z-score:

Decoding multiple variables and disentangling confounds

---

(Notebook)

It often happens that different conditions in an experiment are correlated to each other. For example, in a simple stimulus to action association task (stimulus: A -> action: left; stimulus: B -> action: right), the action performed by a trained subject would clearly be correlated to the presented stimulus.

This correlation makes it hard to drawn conclusions from the results of a decoding analysis, as a good performance for one variable could in fact be due to the recorded activity responding to the other variable: in the example above, one would be able to decode action from a brain region that only represents stimulus, and viceversa.

To disentangle variables from each other and avoid the confounding effect of correlated conditions, Decodanda implements a multi-variable balanced sampling in the decode() function. In practice, the traning and testing data are sampled by making sure that all the values of the other variables are balanced.

Taking from the example above, the decode() function will first create training and testing data for stimulus: A and stimulus: B, each containing a 50%-50% mix of action: left and action: right. It will then run the cross-validated decoding analysis as explained above. The result will therefore be informative on whether the recorded activity responds to the variable stimulus alone, independently on action.

To make Decodanda balance two or more variables, the conditions dictionary must contain two or more key: values associations, each representing a variable name and its two values.

from decodanda import Decodanda

data = {
    'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],   # <TxN array>, neural activations 
    'stimulus': ['A', 'A', 'B', ..., 'B'],             # <Tx1 array>, values of the stimulus variable
    'action': ['left', 'left', 'right', ..., 'left'],  # <Tx1 array>, values of the action variable
    'trial':  [1, 2, 3, ..., T],                       # <Tx1 array>, trial number
}

conditions = {
    'stimulus': ['A', 'B'],
    'action': ['left', 'right']
}

dec = Decodanda(
        data=data,
        conditions=conditions)


# The decode() method will now perform a cross-validated decoding analysis for both variables.
# The multi-variable balanced sampling will ensure that each variable is decoded independently on the other variables.

performances, null = dec.decode(
                        training_fraction=0.5,  # fraction of trials used for training
                        cross_validations=10,   # number of cross validation folds
                        nshuffles=20)           # number of null model iterations

returns:

>>> performances
{'stimulus': 0.84, 'action': 0.53}  # mean decoding performance over the cross_validations folds
>>> null
{'stimulus' [0.55, 0.45 ... 0.52], 'action': [0.54, 0.48, ..., 0.49]}  # 2 x nshuffles (20) values

From which we can deduce that stimulus is represented in the neural activity, while we are not able to decode action better than chance with a linear classifier approach.

Decoding from pseudo-populations data

---

(Notebook)

Decodanda supports pooling from multiple data sets to create pseudo-populations out of the box. To use multiple data sets, just pass a list of dictionaries to the Decodanda constructor:

from decodanda import Decodanda

data1 = {
    'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],   # <T1xN array>, neural activations 
    'stimulus': ['A', 'A', 'B', ..., 'B'],             # <T1x1 array>, labels
    'trial':  [1, 2, 3, ..., T1],                       # <T1x1 array>, trial number
}

data2 = {
    'raster': [[0, 0, ..., 1], ..., [0, 1, ..., 0]],   # <T2xN array>, neural activations 
    'stimulus': ['A', 'B', 'B', ..., 'A'],             # <T2x1 array>, labels
    'trial':  [1, 2, 3, ..., T2],                       # <T2x1 array>, trial number
}
conditions = {
    'stimulus': ['A', 'B']
}

dec = Decodanda(
        data=[data1, data2],
        conditions=conditions)

Note that the two data sets can contain an arbitrary number of trials. However, it is advisable to use the min_trials_per_condition and/or min_data_per_condition keywords of the the Decodanda constructor to ensure that only data sets with enough data are included in the pseudo-population.

For example, if we plan to use 75% of the trials for training and 25% for testing, we want to make sure that each data set included in the analysis contains at least 4 trials (3 for training and 1 for testing). See below for a detailed explanation of these keywords

dec = Decodanda(
        data=[data1, data2],
        conditions=conditions,
        min_trials_per_condition=4,
        min_data_per_condition=10)

performances, null = dec.decode(training_fraction=0.75)

Cross-condition Generalization Performance

---

(Notebook)

First defined in Bernardi et al. (Cell, 2020), the Cross-Condition Generalization Performance (CCGP) is a geometrical measure of how well a classifier trained to decode a variable under specific conditions (values of the other variables) generalizes to new ones. Variables with a high CCGP are called abstract or disentangled.

In geometrical terms, a high CCGP is an indication of a low-dimensional geometry where the coding directions of individual variables are parallel in different conditions. For example, consider a setup where a subject interacts with two stimuli (noted as 1, 2) that can be placed at two specific locations (left, right). The problem is characterized by 2 binary variables identity = {1, 2} and position = {left, right}, for a total of 4 conditions (combinations of varibales).

The relative position of these 4 conditions in the neural activity space defines the representational geometry of the two variables. CCGP, along with decoding performance, can be used as a tool to reveal this geometry:

(image adapted from Boyle, Posani et al. 2023)

Decodanda implements CCGP as a function of the Decodanda class, with a specific null-model that keeps conditions decodable but breaks their geometrical relationship (see Bernardi et al. 2020, Boyle, Posani et al. 2023):

from decodanda import Decodanda

# data has the following structure
#     'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],  
#     'identity': ['1', '2', '1', ..., '1']             
#     'position': ['left', 'right', 'left', ..., 'left'],       
#     'trial':  [1, 2, 3, ..., T],                       
# 

conditions = {
    'identity': ['1', '2'],
    'position': ['left', 'right']
}

dec = Decodanda(
        data=data,
        conditions=conditions)

perf, null = dec.CCGP(nshuffles=20)

returns:

>>> perf
{'identity': 0.72, 'position': 0.68}  # generalization performance for each variable across the other one
>>> null
{'identity' [0.58, 0.41 ... 0.52], 'position': [0.57, 0.43, ..., 0.44]}  # 2 x nshuffles (20) values

with plot=True it will return this visualization:

Balance data for different decoding analyses to compare performances

---

Say we have a simple experiment where a freely-behaving subject is exploring two objects: [A, B], and we want to track how distinguishable these two objects are in their neural representations through days of learning.

As a first analysis, we could use Decodanda to decode object: A from object: B and get a performance for each day. If the performance increases, we might say the neural representations got better with time.

Maybe we are able to track neurons through days using calcium imaging, but the time of interactions with either A or B can vary a lot depending on the subject's engagement on each specific day. How do we compare decoding performances through time if the amount of data varies significantly?

To allow for meaningful comparison between different data sets we need to balance the amount of data in each condition across data sets. This can be done by using the balance_decodandas() function before calling the decode() pipeline:

from decodanda import Decodanda, balance_decodandas

dec_day1 = Decodanda(
  data=data_day_1,
  conditions={'object': ['A', 'B']})

dec_day2 = Decodanda(
  data=data_day_2,
  conditions={'object': ['A', 'B']})

# Balance the two decodandas:
balance_decodandas([dec_day1, dec_day2])

decoding_params = {
  'training_fraction': 0.75,  
  'cross_validations': 10,   
  'nshuffles': 20            
}
perf_day1, null_day1 = dec_day1.decode(**decoding_params)
perf_day2, null_day2 = dec_day2.decode(**decoding_params)

Define conditions using functional syntax

---

Sometimes conditions might be more complex that just a discrete label. For example, we might want to decode data that falls into two continuous intervals of some variable, or we might need to select the data using multiple intersecting criteria.

Decodanda supports the use of functional syntax (e.g., lambda functions) to define conditions. This gives the complete flexibility of using any combination of criteria to select the data belonging to the two decoded classes, as long as these clauses do not intersect.

In the following example, we want to decode a position (a continuous variable) in the two intervals defined as left := [0.00 - 0.25] and right := [0.75 - 1.00].

Additionally, we want to select only data where the animal is running, defined as data['velocity'] > 0.1 in this hypothetical data set):

from decodanda import Decodanda

# Dataset

data = {
    'raster': [[0, 1, ..., 0], ..., [0, 0, ..., 1]],
    'position': [0.11, 0.14, 0.18, ..., 0.94],
    'velocity': [0.05, 0.11, 0.2, ... 0.05]
    'trial':  [1, 2, 3, ..., 100],
}

# Using lambdas to define conditions:

conditions = {
    'Position': {
      'left': lambda d: (d['position'] < 0.25) & (d['velocity'] > 0.1),
      'right': lambda d: (d['position'] > 0.75) & (d['velocity'] > 0.1)
    }
}

# This part of the code stays the same

dec = Decodanda(
        data=data,
        conditions=conditions)

perfs, null = dec.decode(training_fraction=0.9, 
                         nshuffles=25, 
                         cross_validations=10)

Main objects

Decodanda() main constructor parameters

parameter	type	description
data	dict or list of dicts	The data used to decode, organized in dictionaries. Each data dictionary object must contain - one or more variables and values we want to decode, each in the format <var name>: <Tx1 array of values> -raster: <TxN array> the neural features from which we want to decode the variable values - a trial: <Tx1 array> the number that specify which chunks of data are considered independent for cross validation if more than one data dictionaries are passed to the constructor, Decodanda will create pseudo-population data by combining trials from the different dictionaries.
conditions	dict	A dictionary that specifies which values for which variables of data we want to decode, in the form {key: [value1, value2]} If more than one variable is specified, Decodanda will balance all conditions during each decoding analysis to disentangle the variables and avoid confounding correlations.
classifier	Possibly a scikit-learn classifier, but any object that exposes .fit(), .predict(), and .score() methods should work. default: sklearn.svm.LinearSVC	The classifier used for all decoding analyses
neaural_attr	string default: 'raster'	The key of the neural features in the data dictionary
trial_attr	string or None default: 'trial'	The key of the trial attribute in the data dictionary. Each different trial is considered as an independent sample to be used in the cross validation routine, i.e., vectors with the same trial number always goes in either the training or the testing batch. If None: each contiguous chunk of the same values of all variables will be considered an individual trial.
squeeze_trials	bool default: False	If True, all population vectors corresponding to the same trial number for the same condition will be squeezed into a single average activity vector.
trial chunk	int or None default: None	Only used when trial_attr=None. The maximum number of consecutive data points with the same value of all variables that are numbered with the same trial number.
exclude_contiguous_chunks	bool default: False	Only used when trial_attr=None and trial_chunks != None. Discards trials, defined as chunks of trial_chunk data each with the same variable values, that are consecutive in time. Useful to avoid decoding temporal artifacts when there are long auto-correlation times in the neural activations (e.g., calcium imaging)
min_data_per_condition	int default: 2	The minimum number of data points per each condition, defined as a specific combination of variable values, that a data set needs to have to be included in the analysis. In the case of pseudo-simultaneous data, datasets that do not meet this criterion will be excluded from the analysis. If no datasets meet the criterion, the constructor will raise an error.
min_trials_per_condition	int default: 2	The minimum number of unique trial numbers per each condition, defined as a specific combination of variable values, that a data set needs to have to be included in the analysis. In the case of pseudo-simultaneous data, datasets that do not meet this criterion will be excluded from the analysis. If no datasets meet the criterion, the constructor will raise an error.
exclude_silent	bool default: False	Excludes all silent population vectors (only zeros) from the analysis.
verbose	bool default: False	If True, prints most operations and analysis results.
fault_tolerance	bool default: False	If True, raises a warning instead of an error when no datasets meet the inclusion criteria.

Decodanda.decode() main parameters

parameter	type	description
training_fraction	float	The fraction of unique trial numbers used for training the classifier. The remaining trials are used to test the classifier and determine decoding performance.
cross_validations	int default: 10	The number of different training-testing splits for cross-validation.
n_shuffles	int default: 25	The number of null-model iterations of the decoding procedure.
ndata	int or string default: 'auto'	The number of data points (population vectors) sampled for training and for testing for each condition.
non_semantic	bool default: False	If True, Also dichotomies that do not correspond to single variables are decoded (e.g., XOR for two variables).
plot	bool default: False	If True, a visualization of the decoding results is shown.
ax	matplotlib.axis or None default: None	if specified and plot=True, the results will be duplayed in the specified axis instead of a new figure.
return_CV	bool default: False	if True, invidual cross-validation values are returned in a list. Otherwise, the average performance over the cross-validation folds is returned.

Decodanda.CCGP() main parameters

parameter	type	description
resamplings	int default: 5	The number of iterations for each decoding analysis. The returned performance value is the average over these resamplings.
n_shuffles	int default: 25	The number of null-model iterations of the decoding procedure. The geometrical null model for CCGP keeps variables decodable but breaks any geometrical structure re-arranging conditions in the neural activity space. See Bernardi et al 2020 & Boyle,vPosani et al. 2023 for more details.
ndata	int or string default: 'auto'	The number of data points (population vectors) sampled for each condition during all training and testing routines.
plot	bool default: False	If True, a visualization of the CCGP results is shown.
ax	matplotlib.axis or None default: None	if specified and plot=True, the results will be duplayed in the specified axis instead of a new figure.