Deep Learning in Practice

Chapter 4: Small or noisy data: forms of weak supervision

• Data augmentation
• Multi-tasking
• Transfer learning

• Semi-supervision
• Weak supervision
• Self-supervision
• Active learning
  • Local methods
  • Global methods

• Denoising auto-encoder
• Classification with noisy labels
• Regression with noisy labels

I - Small data

Data augmentation

• Add various transformations to real data (possibly random, not using exactly the same transformation twice on the same sample, in order not to learn to biases due to the transformations)
  • eg: for image classification tasks: rotations, flips, contrast, color balance, noise...
  • or also: smooth deformations (replacing image $A$ with $A \circ f$)
• or use a simulator

Multi-tasking

• If too unrelated tasks: training both with the same network will decrease result quality (as the tasks will fight each other to get relevant features for them)
• If related enough tasks: increase in accuracy for the real targeted task (as some features useful for the auxiliary task are useful for it also)
• Example: on a satellite image to cadaset map registration task, learn also to segment images $\implies$ both tasks get better accuracies when trained together

Transfer learning

• pick VGG already trained on ImageNet,
• replace the last layers by your own,
• train them for your own task on your dataset
• $\Leftrightarrow$ considering the before-last layer of VGG as features
• $\implies$ surprisingly, sometimes, such seemingly-different tasks are in fact close enough for this to work (in both cases, develop features for image analysis)

• if very small data, big help in getting relevant features
• if not that small data: big boost in training time, but not necessarily any accuracy gain if trained until convergence:
  [Rethinking ImageNet pre-training; Kaiming He, Ross Girshick, Piotr Dollár; ICCV 2019]

II - Few labeled examples: forms of weak supervision

Semi-supervision

• common unsupervised learning for all data (get clusters, features...) then train supervisedly;
• train supervisedly and label some of the unlabeled samples; iterate (issue: might make mistakes, that will get emphasized with time);
• train supervisedly but check classifier properties on whole dataset (bias, density, margin...)

Weak supervision

Self-supervision

• for an image classification task:
  image puzzle : cut each image into 9 pieces (3x3 grid), then take two pieces randomly (of the same image), and ask their relative location
  [Unsupervised Visual Representation Learning by Context Prediction; Carl Doersch, Abhinav Gupta, Alexei A. Efros; ICCV 2015]
• rotate images by random angles and ask, for each given rotated image, to retrieve that angle
  [Unsupervised Representation Learning by Predicting Image Rotations; Spyros Gidaris, Praveer Singh, Nikos Komodakis; ICLR 2018]
• define many new very specific classes as one per sample in the training set; add random transformations to images and ask which were the original images in the training set, i.e. predict the specific class
  [Discriminative Unsupervised Feature Learning with Exemplar Convolutional Neural Networks; Alexey Dosovitskiy, Philipp Fischer, Jost Tobias Springenberg, Martin Riedmiller, Thomas Brox; NIPS 2014]
• for a video classification task:
  predict next video frame, or, weaker: can this frame lie between these 2?

• [Clusterfit: Improving Generalization of Visual Representations; Xueting Yan, Ishan Misra, Abhinav Gupta, Deepti Ghadiyaram, Dhruv Mahajan; CVPR 2020] : pre-trained network (for a dummy self-supervised task) $\rightarrow$ get features from it (activities in a certain layer) $\rightarrow$ cluster $\rightarrow$ make fake labels $\rightarrow$ train new network for that. More robust to features specific to the dummy task.
• DINO, from [Emerging Properties in Self-Supervised Vision Transformers; Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, Armand Joulin; ICCV 2021] : consider a randomly initialized network (the student), and a copy of it (the teacher). During training, the teacher weights will be a moving average of the student weights (i.e. its weights at the last time steps t, t-1, t-2...). The teacher will thus not be trained at all. Each sample is augmented (rotations, etc.) to produce several "views"; the student is applied to (cropped versions of) such augmented data and is asked to try to reproduce the teacher output on (another, non-cropped view of) the same sample. Thus the student tries to be invariant to the noise due to augmentation, and tries to infer global properties from more local ones (infer the output for a full, non-cropped sample when seeing a cropped version of it). Supplementary considerations are needed to avoid model collapse (e.g., just outputting always 0). This unsupervised pretraining, followed by the training of just a linear classifier or k-NN, yields performance on ImageNet classification close to supervised training.

Active learning

• a large dataset $(x_1, x_2... x_n)$ is given
• with labels known only for a small quantity of samples: $(y_1, y_2... y_p)$ with $p \ll n$
• which $x_i$ (i.e. which $i \in ]p, n]$) to pick and ask to sample?
• one can be based on the predictions by the current model for all unlabeled samples: $\hat{y}_i$, which, in a classification task case, are probability vectors for each sample $i$: $\hat{y}_i = (\hat{y}^c_i)_{c \in C}$ where $C$ is the set of classes.

Local methods

• Uncertainty sampling:
  pick the sample $x_i$ for which the model is the most uncertain, i.e. with lowest prediction confidence: $$\argmin_i\;\; \sup_{c \in C}\;\; \hat{y}^c_i$$
• Margin sampling:
  quantity uncertainty by the difference between the highest classes probabilities: $$\argmin_i\;\; \hat{y}^{c1}_i - \hat{y}^{c2}_i $$ where $c1$ and $c2$ are the two most probable classes for sample $i$, i.e. $c1 = \argmax_c \hat{y}^{c}_i\;$ and $\;c2 = \argmax_{c \neq c1} \hat{y}^{c}_i$
  
• Entropy sampling:
  entropy is maximum when the probability distribution $\hat{y}^c_i$ over classes $c$ is uniform, i.e. most uncertain to pick a class; while minimum when a Dirac peak on a class, i.e. most certain
  $$\argmax_i\;\; H(\hat{y}^{c}_i) \;\;\;\text{ where } H \text{ is the entropy: } \;\; H(\hat{y}^{c}_i) = - \sum_c \hat{y}^{c}_i \log \hat{y}^{c}_i $$
• Query by committee
  Suppose your model is actually an ensemble of $K$ models $m_k$ (for $k \in [1, K]$), trained on the same data, but possibly making different predictions $y_{i,k}$.
  A possible way to quantify uncertainty for one sample $x_i$ is to check how much the predictions $y_{i,k}$ differ for the different models.
  Then, select the point $x_i$ for which the models disagree the most.

Global methods

• Expected model change
  Which new labeled sample would change the current model the most, if doing one supplementary gradient descent step on the parameters $\theta$ of the model to minimize its prediction error?
  $\implies$ which sample would induce the biggest variation of model parameters?
  $\rightarrow$ approximated as the norm of the gradient of the loss for that sample
  with expectation over probabilities of what that label could be:
  $$\argmax_i\;\; \sum_c \; \hat{y}^{c}_i \; \|\nabla_\theta \, \text{Loss}(\hat{y}^c_i, \delta_c)\|$$ noting that $\hat{y}^c_i$ depends on $\theta$, and denoting by $\delta_c$ the Dirac peak on class $c$.
  
• Expected error or uncertainty reduction
  How much is the error (or uncertainty) prediction for all samples reduced if we re-train with that supplementary label?
  $$\argmin_i\;\; \sum_{c \in C} \; \hat{y}^c_i \; \sum_j \text{error prediction for } x_j \text{ if trained with } (x_i, y^c_i) \text{ also}$$ All previous possible ways to quantify uncertainty or error...
  Retrain model, or get the gradient of the error prediction, i.e. e.g. $\nabla_\theta \, \text{Loss}(\hat{y}^{c'}_j, \delta_{c'})$, averaged over possible classes $c'$ for $x_j$, averaged over samples $x_j$, and multiplied by the parameter shift induced by the new sample $-\nabla_\theta \, \text{Loss}(\hat{y}^c_i, \delta_c)$: $$\argmax_i\;\; \sum_{c \in C} \; \hat{y}^c_i \; \sum_j \; \sum_{c' \in C} \hat{y}^{c'}_j \; \nabla_\theta \, \text{Loss}(\hat{y}^{c'}_j, \delta_{c'}) \;\cdot\; \nabla_\theta \, \text{Loss}(\hat{y}^c_i, \delta_c)$$ $\implies$ lots of computations but still linear in the dataset size
  NB: this is precisely the notion of similarity we will study in the noisy data section
  
  
• Density-Weighted Methods
  Searching for samples representatives of many other ones (while on the opposite, most uncertain sample might be irrelevant for other samples)
  $$\argmax_i\;\; [\text{information brought by } (x_i, y_i) ] \times \sum_j \text{similarity}(x_i,x_j)$$ where "information brought" denotes any of the previous methods (to quantity uncertainty or error at $x_i$) and "similarity" is defined appropriately
  NB: with the right choices, this can actually boil down to the same formula as the previous method.

III - Noisy data

Denoising auto-encoder

• originally meant to robustify auto-encoders (without requiring few middle neurons)
• get noisy inputs (in the article, artificial additional noise), ask for reconstruction without noise
• learns to get robust features and to denoise

Classification with noisy labels

Regression with noisy labels

• data self-realignment : possible?
• example: registering RGB satellite images to cadaster maps (binary pictures indicating building presence): no exact ground truth available (spurious deformations in data acquisition & elevation landscape / human mistakes in making cadasters)
  • [Aligning and Updating Cadaster Maps with Aerial Images by Multi-Task, Multi-Resolution Deep Learning; Nicolas Girard, Guillaume Charpiat, Yuliya Tarabalka; ACCV 2018]
  • [Noisy Supervision For Correcting Misaligned Cadaster Maps Without Perfect Ground Truth Data; Nicolas Girard, Guillaume Charpiat, Yuliya Tarabalka; 2019]
    
    
    
• in the case of a regression task : $x \mapsto y$ with noisy dataset samples $(x,y)$ :
  • if output noise (on $y$) is ~i.i.d. (does not depend on x)
    or more exactly: if "relatively similar" $x, x'$, which should have the same true label, have independent noises on two labels $y, y'$
    then noise is unbiased
  • Extreme case of only one possible input $x$, seen many times with different noisy labels $y_i$:
    if loss = $L_2$ metric : $\sum_i \| \hat{y}(x) - y_i \|^2$ with $y_i = y \;\text{real}$ + unknown $\text{noise}_i$
    then the optimal $\hat{y}(x)$ is reached at the mean of $y_i$, i.e. $y$ real $\pm O(\frac{1}{\sqrt{\text{number of samples}}})$
    [Noise2Noise: Learning Image Restoration without Clean Data; Jaakko Lehtinen, Jacob Munkberg, Jon Hasselgren, Samuli Laine, Tero Karras, Miika Aittala, Timo Aila; 2018]
  • General case of different inputs: requires a notion of similarity between any $x$ and $x'$
    $\rightarrow$ defined and studied in [Input similarity from the neural network perspective; G. Charpiat, N. Girard, L. Felardos and Y. Tarabalka; NeurIPS 2019]
    $\implies$ similarity between $x$ and $x'$: based on $\nabla_\theta\, \hat{y}(x) \,\cdot\, \nabla_\theta\, \hat{y}(x')$ (how much a variation of parameters meant to change the labels of point $x$ would affect the labels of point $x'$ too) $\implies$ gives the expected magnitude of the denoising effect for a given trained neural network, without knowing true labels
    $\implies$ linked to the Neural Tangent Kernel (NTK)
  • in practice: denoise the dataset this way (here, re-align) and then re-learn from the aligned dataset (as less noise $\implies$ better results [theoretically same global optimum, but with different confidence (= variance)])