cits package

Submodules

cits.methods module

cits.methods.causaleff_lscm(g, data)[source]

Assigns weights to edges in the unrolled graph estimate of CITS algorithm

Parameters

  • g (networkx.DiGraph) – Unrolled causal graph

  • data (nump.array) – Transformed original time series X by data_transformed function

Returns

Adjacency matrix with (i,j) entry having the weight of causal relationship from the variable with index i \(\rightarrow\) the variable with index j in the unrolled graph g

Return type

numpy.array

cits.methods.cits_full(X, tau, alpha=0.05, cond_dep='cond_dep_pcorr')[source]

Convenient wrapper for CITS algorithm in computing the unweighted rolled graph from time series data. See cits_full_weighted to compute the weighted rolled graph.

Parameters

  • X (nump.array) – pxT array for time series with p variables and T time points

  • tau (int) – Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

  • alpha (float) – Significance level of conditional dependence tests (default is 0.05)

  • cond_dep (string) – Specifies which conditional dependence test to use. It can take value ‘cond_dep_pcorr’ for Partial correlation based test suitable for Gaussian noise distribution and ‘cond_dep_hsic’ for test based on Hilbert-Schmidt criterion applicable for either Gaussian or non-Gaussian noise distributions. Partial correlation based test would be more powerful if the noise distribution is known to be Gaussian. (default is ‘cond_dep_pcorr’)

Returns

Unweighted adjacency matrix of rolled graph

Return type

numpy.array (shape is (p,p))

cits.methods.cits_full_weighted(X, tau, alpha=0.05, cond_dep='cond_dep_pcorr', thresh=10)[source]

Convenient wrapper for CITS algorithm in computing the weighted rolled graph from time series data.

Instead, if you like to compute the unweighted rolled graph, see cits_full. Or alternatively, process the output of this current function to have non-zero edge weights indicating an edge and zero edge weights indicating no edge in the unweighted rolled graph.

Parameters

  • X (nump.array) – pxT array for time series with p variables and T time points

  • tau (int) – Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

  • alpha (float) – Significance level of conditional dependence tests (default is 0.05)

  • cond_dep (string) – Specifies which conditional dependence test to use. It can take value ‘cond_dep_pcorr’ for Partial correlation based test suitable for Gaussian noise distribution and ‘cond_dep_hsic’ for test based on Hilbert-Schmidt criterion applicable for either Gaussian or non-Gaussian noise distributions. Partial correlation based test would be more powerful if the noise distribution is known to be Gaussian. (default is ‘cond_dep_pcorr’)

Returns

Weighted adjacency matrix of rolled graph, whose (i,j) entry represents the weight of causal relationships from variable i \(\rightarrow\) variable j. A non-zero weight indicates the presence of a causal relationship and zero weight indicates its absence.

Return type

numpy.array (shape is (p,p))

cits.methods.cits_rolled(A, p, tau)[source]

Step in the CITS algorithm to transform the unrolled causal graph to rolled graph

Parameters

  • p (int) – # of variables

  • A (numpy.array) – Adjacency matrix of unrolled graph

  • tau (int) – Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

Returns

Adjacency matrix of rolled graph

Return type

numpy.array

cits.methods.cits_unrolled(X, tau, alpha=0.05, cond_dep='cond_dep_pcorr')[source]

Step in the CITS algorithm to estimation the unrolled causal graph step from time series data

Parameters

  • X (numpy.array) – pxT array with p variables and T time points

  • tau (int) – Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

  • alpha (float) – Significance level of conditional dependence tests (default is 0.05)

  • cond_dep (string) – Specifies which conditional dependence test to use. It can take value ‘cond_dep_pcorr’ for Partial correlation based test suitable for Gaussian noise distribution and ‘cond_dep_hsic’ for test based on Hilbert-Schmidt criterion applicable for either Gaussian or non-Gaussian noise distributions. Partial correlation based test would be more powerful if the noise distribution is known to be Gaussian. (default is ‘cond_dep_pcorr’)

Returns

Adjacency matrix of unrolled graph

Return type

numpy.array

cits.methods.cits_weighted_rolled(A, p, tau)[source]

Step in the CITS algorithm to transform the weighted unrolled causal graph to the weighted rolled graph

Parameters

  • A (numpy.array) – Adjacency matrix of weighted unrolled graph

  • p (int) – # of variables

  • tau (int) – Markovian order

Returns

Adjacency matrix of weighted rolled graph

Return type

numpy.array

cits.methods.cond_dep_hsic(chi, i1, j1, k, p, alpha=0.05, reps=10)[source]

Convenient wrapper for conditional dependence test based on Hilbert-Schmidt criterion

cits.methods.cond_dep_pcorr(chi, i1, j1, k, p, alpha=0.05)[source]

Conditional dependence test based on partial correlation

cits.methods.data_transform(X, tau)[source]

Transforms data X of shape (p,T) to time-windowed samples \(\chi\) of shape \((p*2*(\tau+1),N)\), where \(N = \lfloor \frac{T-2*(\tau+1)}{2*(\tau+1)} \rfloor\).

Parameters

X (numpy.array) – pxT array with p variables and T time points

Tau

Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

Returns

Transformed dataset which is an array of shape \((p*2*(\tau+1),N)\)

Return type

numpy.array

cits.methods.data_transformed(X, tau)[source]

Transforms data X of shape (p,n) to time-windowed samples of shape \((N,p*(\tau+1))\), with an inter-sample time gap of \(\tau+1\), where \(N = \lfloor \frac{n-2*(\tau+1)}{2*(\tau+1)} \rfloor\).

Parameters

  • X (numpy.array) – pxT array with p variables and T time points

  • tau (int) – Markovian order, in other words, maximum time delay of interaction, i.e. \(X_t\) can depend up to \(X_{t-\tau}\) and not earlier.

Returns

Transformed dataset which is an array of shape \((N,p*(\tau+1))\)

Return type

numpy.array

cits.methods.hsic_condind(A, B, S, data, reps)[source]

Computes p-value of conditional dependence test based on Hilbert-Schmidt criterion

cits.methods.partial_corr(A, B, S, data)[source]

Computes partial correlation of variables A and B given S based on data.

Parameters

  • A (int) – index of one variable

  • B (int) – index of another variable

  • S (set) – indices of conditioning variables

  • data (numpy.array shape of data should be (# of variables, # of samples)) – Dataset with samples for the variables

Returns

Partial correlation of A and B given S based on data

Return type

float

cits.methods.powerset(iterable)[source]

powerset([1,2,3]) = \(\{(), (1,), (2,), (3,), (1,2), (1,3), (2,3), (1,2,3)\}\)

cits.simulate_timeseries module

cits.simulate_timeseries.simulate(model, noise, T)[source]

Simulate time series from different models and ground truth adjacencies for time series causal graph.

Parameters

  • model (string) – Model for simulation. It take one of the these values: ‘lingauss1’ for Linear Gaussian Model 1, ‘lingauss2’ for Linear Gaussian Model 2, ‘nonlinnongauss1’ for Non-linear Non-Gaussian Model 1, ‘nonlinnongauss2’ for Non-linear Non-Gaussian Model 2, ‘ctrnn’: CTRNN

  • noise (float) – Noise standard deviation in the simulation

  • T (int) – Number of time points to have in the simulated time series

Returns

a tuple of three numpy.array as follows. first numpy.array : Simulated time series of shape (4,T) with T time-recordings for 4 variables. second numpy.array : Grouth truth unweighted adjacency matrix: (i,j) entry represents causal influence from i->j. third numpy.array : Grouth truth weighted adjacency matrix: (i,j) entry has the strength of causal influence from i->j.

Return type

tuple

cits.simulate_timeseries.simulate_ctrnn(T, n_vars, w, tau, noise=1)[source]

Simulate a continuous time recurrent neural network (CTRNN) time series

Parameters

  • T (int) – Number of time points to have in the simulated time series

  • n_vars (int) – Number of variables to have in the simulated time series

  • w (numpy.array) – Weights of the CTRNN

  • tau (float) – Time constant of the CTRNN

  • noise (float) – Noise standard deviation in the simulation

Returns

Simulated time series of shape (n_vars,T) with T time-recordings for n_vars many variables

Return type

numpy.array