How to determine image classification feasibility

Problem Statement

For classification machine learning tasks, there is an inherent difficulty associated with signal to noise ratio in the images. One way of quantifying this difficulty is the Bayes Error Rate, or irreducable error. This metric tells you if it would be feasible to use a given feature set to predict a target variable.

DataEval has introduced a method of calculating this error rate that uses image embeddings.

When to use

The BER metric should be used when you would like to measure the feasibility of a machine learning task. For example, if you have an operational accuracy requirement of 80%, and would like to know if this is feasibly achievable given the imagery. A low feasibility score will tell you that the problem you are trying to score cannot be solved with the existing data at the accuracy you desire. This in turn implies that your question does not follow a learnable pattern or that your data is noisy.

What you will need

  1. A set of image embeddings and their corresponding class labels. This requires training an autoencoder to compress the images.

  2. A Python environment with the following packages installed:

    • dataeval

Setting up

Let’s import the required libraries needed to set up a minimal working example

import numpy as np
from maite_datasets.image_classification import MNIST

from dataeval import Embeddings, Metadata
from dataeval.config import set_seed
from dataeval.core import ber_mst
from dataeval.selection import ClassBalance, ClassFilter, Limit, Select

set_seed(42)  # For reproducibility

Loading in data

While you can use your own dataset, for this example we imported the MNIST dataset and will use it going forward. It was imported from the DataEval utils package.

To highlight the effects of modifying the dataset on its Bayes Error Rate, we will only include a subset of 6,000 images and their labels for digits 1, 4, and 9

# Configure the dataset transforms
transforms = [
    lambda x: x / 255.0,  # scale to [0, 1]
    lambda x: x.astype(np.float32),  # convert to float32
]

# Load the train set of the MNIST dataset and apply transforms
train_ds = MNIST(root="./data/", image_set="train", transforms=transforms, download=True)

# Get the indices of the first 2000 samples for labels 1, 4, and 9
train_ds = Select(train_ds, selections=[Limit(6000), ClassFilter((1, 4, 9)), ClassBalance("interclass")])

# Split out the embeddings and labels
embeddings = Embeddings(train_ds, batch_size=64)
labels = Metadata(train_ds).class_labels

print(train_ds)

Select Dataset
--------------
    Selections: [Limit(size=6000), ClassFilter(classes=(1, 4, 9), filter_detections=True), ClassBalance(_method=interclass, num_samples=None, background_class=None, num_empty=None, agg_fn=mean, oversample_factor=1.0, minimize_duplicates=False, _rng=Generator(PCG64), _num_images=18533, _empty=0, images_per_class={4: [0, 5, 8, 12, 18, 21, 23, 24, 25, 33, 34, 42, 45, 47, 50, 51, 52, 57, 58, 59, 68, 75, 76, 81, 85, 90, 91, 92, 97, 99, 100, 101, 106, 110, 112, 113, 114, 120, 125, 128, 129, 130, 132, 133, 140, 144, 145, 146, 153, 155, 162, 167, 180, 184, 189, 191, 194, 197, 200, 206, 207, 209, 217, 219, 220, 221, 224, 226, 227, 230, 231, 233, 235, 239, 240, 242, 245, 247, 249, 250, 262, 264, 272, 274, 277, 278, 279, 280, 281, 282, 286, 287, 290, 291, 292, 296, 297, 300, 304, 307, 311, 316, 317, 318, 319, 323, 325, 326, 330, 333, 336, 345, 346, 352, 354, 355, 357, 366, 371, 373, 375, 376, 379, 380, 383, 385, 387, 390, 392, 394, 396, 397, 398, 400, 402, 407, 410, 412, 414, 415, 417, 419, 421, 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18472: [4], 18473: [9], 18474: [1], 18475: [4], 18476: [9], 18477: [9], 18478: [1], 18479: [4], 18480: [1], 18481: [9], 18482: [1], 18483: [9], 18484: [1], 18485: [1], 18486: [4], 18487: [1], 18488: [9], 18489: [9], 18490: [4], 18491: [4], 18492: [1], 18493: [1], 18494: [4], 18495: [4], 18496: [4], 18497: [1], 18498: [9], 18499: [9], 18500: [9], 18501: [4], 18502: [9], 18503: [4], 18504: [1], 18505: [4], 18506: [9], 18507: [1], 18508: [4], 18509: [9], 18510: [1], 18511: [4], 18512: [9], 18513: [4], 18514: [1], 18515: [4], 18516: [9], 18517: [4], 18518: [9], 18519: [4], 18520: [9], 18521: [4], 18522: [1], 18523: [1], 18524: [1], 18525: [9], 18526: [9], 18527: [4], 18528: [1], 18529: [1], 18530: [9], 18531: [9], 18532: [1]}, _cls_frq={4: 0.3152214967895106, 1: 0.36378352128635405, 9: 0.32099498192413534}, _empty_image_indices=[], classes=[4, 1, 9])]
    Selected Size: 6000

MNIST Dataset
-------------
    Corruption: None
    Transforms: [<function BaseDataset._wrap_transform.<locals>.wrapper at 0x7e397f6db600>, <function BaseDataset._wrap_transform.<locals>.wrapper at 0x7e397f6db740>]
    Image Set: train
    Metadata: {'id': 'MNIST_train', 'index2label': {0: 'zero', 1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five', 6: 'six', 7: 'seven', 8: 'eight', 9: 'nine'}, 'split': 'train'}
    Path: /builds/jatic/aria/dataeval/docs/source/notebooks/data/mnist
    Size: 60000

print("Number of training samples: ", len(embeddings))
print("Image shape:", embeddings.shape)
print("Label counts: ", np.unique(labels, return_counts=True))

Number of training samples:  6000
Image shape: (6000, 784)
Label counts:  (array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), array([603, 684, 578, 557, 663, 503, 622, 640, 535, 615]))

We have taken a subset of the data that is only the digits 1, 4, and 9. The BER estimate requires 1 dimension, that’s why we have flattened images. This is ok since MNIST images are small, in practice we would need to do some dimension reduction (autoencoder) here.

We now have 6,000 flattened images of size 784. Next we can move on to evaluation of the dataset.

Evaluation

Suppose we would like to build a classifier that differentiates between the handwritten digits 1, 4, and 9 with predetermined accuracy requirement of 99%.

We will use BER to check the feasibility of the task. As the images are small, we can simple use the flattened raw pixel intensities to calculate BER (no embedding necessary). Note: This will not be the case in general.

# Evaluate the BER metric for the MNIST data with digits 1, 4, 9.
# One minus the value of this metric gives our estimate of the upper bound on accuracy.
ber_result = ber_mst(embeddings, labels)

print("The bayes error rate estimation:", ber_result["upper_bound"])

The bayes error rate estimation: 0.050666666666666665

The estimate of the maximum achievable accuracy is one minus the BER estimate.

print("The maximum achievable accuracy:", 1 - ber_result["upper_bound"])

The maximum achievable accuracy: 0.9493333333333334

Results

The maximum achievable accuracy on a dataset of 1, 4, and 9 is about 94%. This does not meet our requirement of 99% accuracy!

Modify dataset classification

To address insufficient accuracy, lets modify the dataset to classify an image as “1” or “Not a 1”. By combining classes, we can hopefully achieve the desired level of attainable accuracy.

# Creates a binary mask where current label == 1 that can be used as the new labels
labels_merged = labels == 1
print("New label counts:", np.unique(labels_merged, return_counts=True))

New label counts: (array([False,  True]), array([5316,  684]))

# Evaluate the BER metric for the MNIST data with updated labels
new_result = ber_mst(embeddings, labels_merged)

print("The bayes error rate estimation:", new_result["upper_bound"])

The bayes error rate estimation: 0.008833333333333334

The estimate of the maximum achievable accuracy is one minus the BER estimate.

print("The maximum achievable accuracy:", 1 - new_result["upper_bound"])

The maximum achievable accuracy: 0.9911666666666666

Results

The maximum achievable accuracy on a dataset of 1 and not 1 (4, 9) is about 99%. This does meet our accuracy requirement.

By using BER to check for feasibility early on, we were able to reformulate the problem such that it is feasible under our specifications