# Leakage-Free Fitting, Scaling, and Preprocessing

`D00-F12-A08` · Financial Mathematics, Statistics, and Data Foundations → Statistical Computing and Reproducibility · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/leakage-free-fitting-scaling-and-preprocessing/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { leakageFreeFittingScalingAndPreprocessing } from "fintech-algorithms/foundations/statistical-computing-and-reproducibility/leakage-free-fitting-scaling-and-preprocessing";
```

## Signature

```ts
leakageFreeFittingScalingAndPreprocessing(input)
```

Fits a standardizing centre and scale on the training split alone, then applies that one transform to both splits.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | Reads `train`, at least two finite numbers to fit on, and `test`, the held-out finite numbers to transform. A non-empty `values` list of finite numbers must also be present; it is validated but not used here. |

## Returns

`D00Output`

`fittedMean` and `fittedScale` are the training mean and sample standard deviation, `transformedTrain` and `transformedTest` are both splits centred and scaled by those two figures, and `fitUsedTestData` is always false.

## Errors

- When `values` is absent, empty, or holds a non-finite number — throws RangeError
- When `train` holds fewer than two observations — throws RangeError
- When the training data is constant, so its sample standard deviation is zero — throws RangeError

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`input`:

```json
{
  "values": [1, 2, 3, 4, 5],
  "floatingValue": 0.1,
  "maxSafeMagnitude": 1.7976931348623157e+308,
  "window": 3,
  "rawValues": [1, null, 2, "bad", 3],
  "invalidPolicy": "drop-and-report",
  "seed": 42,
  "sampleCount": 5,
  "leftVector": [
    {
      "index": "A",
      "value": 1
    },
    {
      "index": "B",
      "value": 2
    }
  ],
  "rightVector": [
    {
      "index": "B",
      "value": 20
    },
    {
      "index": "C",
      "value": 30
    }
  ],
  "train": [10, 12, 14, 16],
  "test": [18, 20],
  "actual": [1, 2.0000001, 3],
  "expected": [1, 2, 3]
}
```

Showing 14 of 18 fields.

### Call

```ts
leakageFreeFittingScalingAndPreprocessing(input)
```

### Returns

object with 2 fields: fittedMean, fittedScale

```json
{
  "fittedMean": 13,
  "fittedScale": 2.581988897471611
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/leakage-free-fitting-scaling-and-preprocessing/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/statistical-computing-and-reproducibility/leakage-free-fitting-scaling-and-preprocessing/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt