### Learning as an Attention Optimization Problem

When learning which dimensions of information help us make accurate categorization decisions or rewarding action plans, we pay a premium to attend to the important dimensions and ignore the unimportant dimensions. However, there are many ways in which this prioritization can occur. In this line of work, we develop, compare, and contrast learning theories by subjecting them to different empirical tests using choice responses and eye-tracking data to directly constrain the set of possible attention orientation paths. Although much of the focus has been on learning across trials because the models are mathematically tractable and easy to fit to large data sets, we have also shown that the same learning dynamics occur within a trial as well.

**Representative Publications:**

- Simplicity Biases in Human Learning
- Attention Optimization Represented in the Brain
- Between- and Within-trial Learning Dynamics
- Learning Traps

**Integrating Neural and Behavioral Measures of Cognition**

Scientists who study cognition infer underlying processes either by observing behavior (e.g., response times, percentage correct) or by observing neural activity (e.g., the BOLD response). These two types of observations have traditionally supported two separate lines of study. The first is led by cognitive modelers, who rely on behavior alone to support their computational theories. The second is led by cognitive neuroimagers, who rely on statistical models to link patterns of neural activity to experimental manipulations, often without any attempt to make a direct connection to an explicit computational theory. Our lab develops and uses methods for joining neuroimaging and computational modeling in a single hierarchical framework. Our approach allows the neural data to influence the parameters of the cognitive model and allows behavioral data, even in the absence of neural data, to constrain the neural model. This approach is important because it provides mechanistic insight to brain function, and allows us to interpret neural data through the lens of a cognitive model.

**Representative Publications:**

- Original article
- Extensions to single-trial measures
- Extensions to multi-modal data fusion
- Factor analytic linking functions
- Tutorial with Directed and Covariance Models

**Neural and Mechanistic Bases of Self-Control**

When making decisions, we are often faced with the difficult problem of weighing gains (e.g., money) and losses (e.g., time) of a stimulus to evaluate its attractiveness. Sometimes, incurring a larger loss can result in a larger gain, such as investments which take longer amounts of time to arrive at larger rewards. However, to hold out for these larger rewards, we require ‘self-control’. The lab is interested in identifying brain networks involved in self control, as well as developing mathematical models that describe how the self-control process is carried out.

**Representative Publications:**

- Neural and mechanistic bases of self-control
- Neural correlates of total value accumulation
- Behavioral modeling of intertemporal choice data

**Dynamic Decision Making**

The lab is also interested in understanding how external factors such as the environment, and internal factors such as working memory interact to shape an observer’s perception of the world, and ultimately how this perception drives their decisions. In general, we use models that can flexibly adapt their underlying representations as a function of the stimuli and model parameters in a way that might be akin to individual observers.

**Representative Publications:**

**Methods for Bayesian Estimation**

Our lab almost exclusively uses Bayesian statistics to estimate parameters of cognitive models. However, it is often the case that the application of Bayesian statistics to these models is difficult, necessitating the development of novel methods to guide the estimation procedure. Our lab has developed a number of tools for approximating the likelihood function in a variety of contexts, partitioning parameter spaces for hierarchical models, and efficiently sampling from posterior distributions.

**Representative Publications:**

- Probability Density Approximation method
- Hierarchical ABC
- Approximate Bayesian Computation with Differential Evolution
- Tutorial on Approximate Bayesian Computation (ABC) methods
- Differential Evolution with Markov chain Monte Carlo
- Book on Likelihood-free Methods for Cognitive Science

**Model Comparison and Evaluation**

As our lab is model-oriented, a fundamental component is establishing model validity, and comparing among different models. To do this, our lab uses two approaches. The first approach compares extant models by fitting them to data, penalizes for model complexity, and compares model performance. The second approach is to develop modeling frameworks, which are unidentifiable by themselves, but can be used to subsume extant theories as well as propose new ones. As each model represents a particular constellation of model mechanisms, our approach is to test whether specific model mechanisms might be better appreciated in the context of other modeling architectures.

**Representative Publications:**

- Models of Episodic Memory
- Models of Perceptual Decision Making
- Models of Intertemporal Choice
- Models of Multimodal Sensory Integration
- Models of Preferential Choice (Context Effects)

**Joint Models for real-time fMRI**

Efficient data collection is one of the most important goals to be pursued in cognitive science experiments, and in the context of neuroimaging studies, the cost of poor data collection is exceptionally high. Using our model-based orientation, the lab has combined the joint modeling framework with Adaptive Design Optimization for fMRI studies. ADO is a Bayesian framework for optimizing the proposal of new stimuli on a trial-by-trial level (Cavagnaro, Myung, Pitt, & Kujala, 2010). The lab is developing ADO for real-time fMRI experiments by using joint models as a way to drive the inferential procedure (see “Integrating Neural and Behavioral Measures of Cognition”). Our lab is also interested in computational issues intertwined with real-time design optimization such as adaptive gridding methods and online estimation of trial-wise brain activity.