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Toolbox for inferring psychological embeddings.

Project description

PsiZ: A Psychological Embedding Package


PsiZ provides the computational tools to infer a continuous, multivariate stimulus representation using ordinal similarity relations. It integrates well-established cognitive theory with contemporary computational methods. The companion Open Access article is available at


The best way to install PsiZ is by cloning from GitHub and installing the local repo using pip.

  1. Use git to clone the latest version: git clone
  2. Install the cloned repo using pip: pip install /local/path/to/psiz

The repository can also be cloned by: * Manually download the latest version at * Use git to clone a specific release, for example: git clone --branch v0.2.2 Alternatively, but not recommended, you can install from PyPI using pip install psiz. The versions available through PyPI lag behind the GitHub version.

Note: PsiZ also requires TensorFlow. The current file fulfills this dependency by downloading the tensorflow package using pip.

Quick Start

There are four predefined embedding models to choose from:

  1. Inverse
  2. Exponential
  3. HeavyTailed
  4. StudentsT

Once you have selected an embedding model, you must provide two pieces of information in order to infer an embedding.

  1. The similarity judgment observations (often abbreviated as obs).
  2. The number of unique stimuli that will be in your embedding.
import psiz

# Load some observations (i.e., judged trials).
(obs, catalog) = psiz.datasets.load('birds-16')
# Initialize an embedding model.
emb = psiz.models.Exponential(catalog.n_stimuli)
# Fit the embedding model using similarity judgment observations.
# Optionally save the fitted model.'my_embedding.h5')

Trials and Observations

Inference is performed by fitting a model to a set of observations. In this package, a single observation is comprised of trial where multiple stimuli that have been judged by an agent (human or machine) based on their similarity.

In the simplest case, an observation is obtained from a trial consisting of three stimuli: a query stimulus (q) and two reference stimuli (a and b). An agent selects the reference stimulus that they believe is more similar to the query stimulus. For this simple trial, there are two possible outcomes. If the agent selected reference a, then the observation for the ith trial would be recorded as the vector:

Di = [q a b]

Alternatively, if the agent had selected reference b, the observation would be recorded as:

Di = [q b a]

In addition to a simple triplet trial, this package is designed to handle a number of different trial configurations. A trial may have 2-8 reference stimuli and an agent may be required to select and rank more than one reference stimulus.

Using Your Own Data

To use your own data, you should place your data in a psiz.trials.Observations object. Once the Observations object has been created, you can save it to disk by calling its save method. It can be loaded later using the function psiz.trials.load(filepath). Consider the following example that uses randomly generated data:

import numpy as np
import psiz.trials

# Let's assume that we have 10 unique stimuli.
stimuli_list = np.arange(0, 10, dtype=int)

# Let's create 100 trials, where each trial is composed of a query and
# four references. We will also assume that participants selected two
# references (in order of their similarity to the query.)
n_trial = 100
n_reference = 4
response_set = np.empty([n_trial, n_reference + 1], dtype=int)
n_select = 2 * np.ones((n_trial), dtype=int)
for i_trial in range(n_trial):
    # Randomly selected stimuli and randomly simulate behavior for each
    # trial (one query, four references).
    response_set[i_trial, :] = np.random.choice(
        stimuli_list, n_reference + 1, replace=False

# Create the observations object and save it to disk.
obs = psiz.trials.Observations(response_set, n_select=n_select)'path/to/obs.hdf5')

# Load the observations from disk.
obs = psiz.trials.load('path/to/obs.hdf5')

Note that the values in response_set are assumed to be contiguous integers [0, N[, where N is the number of unique stimuli. Their order is also important. The query is listed in the first column, an agent's selected references are listed second (in order of selection if the trial is ranked) and then any remaining unselected references are listed (in any order).

Common Use Cases

Selecting the Dimensionality.

By default, an embedding will be inferred using two dimensions. Typically you will want to set the dimensionality to something else. This can easily be done using the keyword n_dim during embedding initialization. The dimensionality can also be determined using a cross-validation procedure

n_stimuli = 100

model_spec = {
    'model': psiz.models.Exponential,
    'n_stimuli': n_stimuli,
    'n_group': 1,
    'modifier': None

search_summary =, model_spec)
n_dim = search_summary['dim_best']

emb = psiz.models.Exponential(n_stimuli, n_dim=4)

Multiple Groups

By default, the embedding will be inferred assuming that all observations were obtained from a single population or group. If you would like to infer an embedding with multiple group-level parameters, use the n_group keyword during embedding initialization. When you create your psiz.trials.observations object you will also need to set the group_id attribute to indicate the group-membership of each trial.

n_stimuli = 100
emb = psiz.models.Exponential(n_stimuli, n_dim=4, n_group=2)

Fixing Free Parameters

If you know some of the free parameters already, you can set them to the desired value and then make those parameters untrainable.

n_stimuli = 100
emb = psiz.models.Exponential(n_stimuli, n_dim=2)
emb.rho = 2.0
emb.tau = 1.0
emb.trainable({'rho': False, 'tau': False})

If you are also performing a dimensionality search, these constraints can be passed in using a post-initialization modifier function.

n_stimuli = 100

def modifier_func(emb):
    emb.rho = 2.0
    emb.tau = 1.0
    emb.trainable({'rho': False, 'tau': False})
    return emb

model_spec = {
    'model': psiz.models.Exponential,
    'n_stimuli': n_stimuli,
    'n_group': 1,
    'modifier': modifier_func

search_summary =, model_spec)
n_dim = search_summary['dim_best']


  • catalog - Class for storing stimulus information.
  • datasets - Functions for loading some pre-defined catalogs and observations.
  • dimensionality - Routine for selecting the dimensionality of the embedding.
  • generator - Generate new trials randomly or using active selection.
  • models - A set of pre-defined pscyhological embedding models.
  • preprocess - Functions for preprocessing observations.
  • simulate - Simulate an agent making similarity judgments.
  • trials - Classes and functions for creating and managing observations.
  • utils - Utility functions.
  • visualize - Functions for visualizing embeddings.


  • Brett D. Roads
  • Michael C. Mozer
  • See also the list of contributors who participated in this project.

What's in a name?

The name PsiZ (pronounced sigh zeee) is meant to serve as shorthand for the term psychological embedding. The greek letter Psi is often used to represent the field of psychology and the matrix variable Z is often used in machine learning to denote a latent feature space.


This project is licensed under the Apache Licence 2.0 - see the LICENSE.txt file for details.


  • van der Maaten, L., & Weinberger, K. (2012, Sept). Stochastic triplet embedding. In Machine learning for signal processing (mlsp), 2012 IEEE international workshop on (p. 1-6). doi:10.1109/MLSP.2012.6349720
  • Roads, B. D., & Mozer, M. C. (2019). Obtaining psychological embeddings through joint kernel and metric learning. Behavior Research Methods. 51(5), 2180-2193. doi:10.3758/s13428-019-01285-3
  • Wah, C., Branson, S., Welinder, P., Perona, P., & Belongie, S. (2011). The Caltech-UCSD Birds-200-2011 Dataset (Tech. Rep. No. CNS-TR-2011-001). California Institute of Technology.

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