squiggle/packages/squiggle-lang/__tests__/TS/SampleSet_test.ts

import { Distribution } from "../../src/js/index";
import { expectErrorToBeBounded, failDefault } from "./TestHelpers";
import * as fc from "fast-check";

// Beware: float64Array makes it appear in an infinite loop.
let arrayGen = () =>
  fc.float32Array({
    minLength: 10,
    maxLength: 10000,
    noDefaultInfinity: true,
    noNaN: true,
  });

describe("cumulative density function", () => {
  let n = 10000;

  // We should fix this.
  test.skip("'s codomain is bounded above", () => {
    fc.assert(
      fc.property(arrayGen(), fc.float(), (xs_, x) => {
        let xs = Array.from(xs_);
        // Should compute with squiggle strings once interpreter has `sample`
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(x).value;
        let epsilon = 5e-7;
        expect(cdfValue).toBeLessThanOrEqual(1 + epsilon);
      })
    );
  });

  test("'s codomain is bounded below", () => {
    fc.assert(
      fc.property(arrayGen(), fc.float(), (xs_, x) => {
        let xs = Array.from(xs_);
        // Should compute with squiggle strings once interpreter has `sample`
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(x).value;
        expect(cdfValue).toBeGreaterThanOrEqual(0);
      })
    );
  });

  test("at the highest number in the sample is close to 1", () => {
    fc.assert(
      fc.property(arrayGen(), (xs_) => {
        let xs = Array.from(xs_);
        let max = Math.max(...xs);
        // Should compute with squiggle strings once interpreter has `sample`
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(max).value;
        let min = Math.min(...xs);
        let epsilon = 5e-3;
        if (max - min < epsilon) {
          expect(cdfValue).toBeLessThan(1 - epsilon);
        } else {
          expect(dist.cdf(max).value).toBeGreaterThan(1 - epsilon);
        }
      })
    );
  });

  // I may simply be mistaken about the math here.
  test.skip("at the lowest number in the distribution is within epsilon of 0", () => {
    fc.assert(
      fc.property(arrayGen(), (xs_) => {
        let xs = Array.from(xs_);
        let min = Math.min(...xs);
        // Should compute with squiggle strings once interpreter has `sample`
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(min).value;
        let max = Math.max(...xs);
        let epsilon = 5e-3;
        if (max - min < epsilon) {
          expect(cdfValue).toBeGreaterThan(4 * epsilon);
        } else {
          expect(cdfValue).toBeLessThan(4 * epsilon);
        }
      })
    );
  });

  // I believe this is true, but due to bugs can't get the test to pass.
  test.skip("is <= 1 everywhere with equality when x is higher than the max", () => {
    fc.assert(
      fc.property(arrayGen(), fc.float(), (xs_, x) => {
        let xs = Array.from(xs_);
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(x).value;
        let max = Math.max(...xs);
        if (x > max) {
          let epsilon = (x - max) / x;
          expect(cdfValue).toBeGreaterThan(1 * (1 - epsilon));
        } else if (typeof cdfValue == "number") {
          expect(Math.round(1e5 * cdfValue) / 1e5).toBeLessThanOrEqual(1);
        } else {
          failDefault();
        }
      })
    );
  });

  test("is non-negative everywhere with zero when x is lower than the min", () => {
    fc.assert(
      fc.property(arrayGen(), fc.float(), (xs_, x) => {
        let xs = Array.from(xs_);
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let cdfValue = dist.cdf(x).value;
        if (x < Math.min(...xs)) {
          expect(cdfValue).toEqual(0);
        } else {
          expect(cdfValue).toBeGreaterThan(0);
        }
      })
    );
  });
});

// I no longer believe this is true.
describe("probability density function", () => {
  let n = 1000;

  test.skip("assigns to the max at most the weight of the mean", () => {
    fc.assert(
      fc.property(arrayGen(), (xs_) => {
        let xs = Array.from(xs_);
        let max = Math.max(...xs);
        let mean = xs.reduce((a, b) => a + b, 0.0) / xs.length;
        // Should be from squiggleString once interpreter exposes sampleset
        let dist = new Distribution(
          { tag: "SampleSet", value: xs },
          { sampleCount: n, xyPointLength: 100 }
        );
        let pdfValueMean = dist.pdf(mean).value;
        let pdfValueMax = dist.pdf(max).value;
        if (typeof pdfValueMean == "number" && typeof pdfValueMax == "number") {
          expect(pdfValueMax).toBeLessThanOrEqual(pdfValueMean);
        } else {
          expect(pdfValueMax).toEqual(pdfValueMean);
        }
      })
    );
  });
});

// // This should be true, but I can't get it to work.
describe("mean is mean", () => {
  test.skip("when sampling twice as widely as the input", () => {
    fc.assert(
      fc.property(
        fc.float64Array({ minLength: 10, maxLength: 100000 }),
        (xs_) => {
          let xs = Array.from(xs_);
          let n = xs.length;
          let dist = new Distribution(
            { tag: "SampleSet", value: xs },
            { sampleCount: 2 * n, xyPointLength: 4 * n }
          );
          let mean = dist.mean();
          if (typeof mean.value == "number") {
            expectErrorToBeBounded(
              mean.value,
              xs.reduce((a, b) => a + b, 0.0) / n,
              5e-1,
              1
            );
          } else {
            failDefault();
          }
        }
      )
    );
  });

  test.skip("when sampling half as widely as the input", () => {
    fc.assert(
      fc.property(
        fc.float64Array({ minLength: 10, maxLength: 100000 }),
        (xs_) => {
          let xs = Array.from(xs_);
          let n = xs.length;
          let dist = new Distribution(
            { tag: "SampleSet", value: xs },
            { sampleCount: Math.floor(n / 2), xyPointLength: 4 * n }
          );
          let mean = dist.mean();
          if (typeof mean.value == "number") {
            expectErrorToBeBounded(
              mean.value,
              xs.reduce((a, b) => a + b, 0.0) / n,
              5e-1,
              1
            );
          } else {
            failDefault();
          }
        }
      )
    );
  });
});