A Reductionist Framework for Human Happiness

Is it possible to define happiness as a set of non-linear basis functions that capture societal interaction effects?

Formalizing Happiness

Sinusoidal Functions: Emotional Battery

Stationarity

Cyclicity

Interactive Complexity

Defining Happiness

Sampling Happiness

Data Generation Summary

Gaussian Processes

Weight Space View

Function Space View

Pyro Mødel

Happiness Data Generation

Aggregate Happiness Process

Let’s take a look at what happiness looks like!

Our AHP: a process that governs one’s happiness at any given time. The dark blue line is the final (convolved) Aggregate Happiness Process. The fainter, dotted, functions are one’s emotional battery (when combined produce the AHP). Access to this underlying process provides insight into one’s emotional state.
Sampled data from the target function. Representing what we might actually observe in an individual.

Model Fitting IN Pyro!

Optimization Methodology + Loss Function

Blue line: the true data generating process (target function). Red line: the predictive model (samples from our GP). Purple Area: credibility (confidence) intervals around out mean estimate (the red line). Purple dots: the data.

Results

Cracking GPs

Left: In a data-sparse environment, the model adequately (and intuitively) learns a smoother functional fit. Right: In areas with insufficient data (no samples) the model captures vast uncertainty.
Left: The data generating process, generate many samples in the first half of the function & very few samples over the span of the second half. A single model fit over both the data-rich & data-sparse environment: note the far smoother, less confident fit over the latter continuum.

Philosophical Consideration

Code

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