5,489 machine learning methods and techniques
The Softmax output function transforms a previous layer's output into a vector of probabilities. It is commonly used for multiclass classification. Given an input vector and a weighting vector we have:
Dense Connections, or Fully Connected Connections, are a type of layer in a deep neural network that use a linear operation where every input is connected to every output by a weight. This means there are parameters, which can lead to a lot of parameters for a sizeable network. where is an activation function. Image Source: Deep Learning by Goodfellow, Bengio and Courville
Dropout is a regularization technique for neural networks that drops a unit (along with connections) at training time with a specified probability (a common value is ). At test time, all units are present, but with weights scaled by (i.e. becomes ). The idea is to prevent co-adaptation, where the neural network becomes too reliant on particular connections, as this could be symptomatic of overfitting. Intuitively, dropout can be thought of as creating an implicit ensemble of neural networks.
A Linear Layer is a projection .
Unlike batch normalization, Layer Normalization directly estimates the normalization statistics from the summed inputs to the neurons within a hidden layer so the normalization does not introduce any new dependencies between training cases. It works well for RNNs and improves both the training time and the generalization performance of several existing RNN models. More recently, it has been used with Transformer models. We compute the layer normalization statistics over all the hidden units in the same layer as follows: where denotes the number of hidden units in a layer. Under layer normalization, all the hidden units in a layer share the same normalization terms and , but different training cases have different normalization terms. Unlike batch normalization, layer normalization does not impose any constraint on the size of the mini-batch and it can be used in the pure online regime with batch size 1.
Label Smoothing is a regularization technique that introduces noise for the labels. This accounts for the fact that datasets may have mistakes in them, so maximizing the likelihood of directly can be harmful. Assume for a small constant , the training set label is correct with probability and incorrect otherwise. Label Smoothing regularizes a model based on a softmax with output values by replacing the hard and classification targets with targets of and respectively. Source: Deep Learning, Goodfellow et al Image Source: When Does Label Smoothing Help?
Absolute Position Encodings are a type of position embeddings for [Transformer-based models] where positional encodings are added to the input embeddings at the bottoms of the encoder and decoder stacks. The positional encodings have the same dimension as the embeddings, so that the two can be summed. In the original implementation, sine and cosine functions of different frequencies are used: where is the position and is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from to . This function was chosen because the authors hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset , can be represented as a linear function of . Image Source: D2L.ai
Sparse Evolutionary Training
Dynamic Sparse Training method where weight mask is updated randomly periodically
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Attention Dropout is a type of dropout used in attention-based architectures, where elements are randomly dropped out of the softmax in the attention equation. For example, for scaled-dot product attention, we would drop elements from the first term:
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Linear Warmup With Linear Decay is a learning rate schedule in which we increase the learning rate linearly for updates and then linearly decay afterwards.
Balanced Selection
Cosine Annealing is a type of learning rate schedule that has the effect of starting with a large learning rate that is relatively rapidly decreased to a minimum value before being increased rapidly again. The resetting of the learning rate acts like a simulated restart of the learning process and the re-use of good weights as the starting point of the restart is referred to as a "warm restart" in contrast to a "cold restart" where a new set of small random numbers may be used as a starting point. Where where and are ranges for the learning rate, and account for how many epochs have been performed since the last restart. Text Source: Jason Brownlee Image Source: Gao Huang
Linear Warmup With Cosine Annealing is a learning rate schedule where we increase the learning rate linearly for updates and then anneal according to a cosine schedule afterwards.
A Concatenated Skip Connection is a type of skip connection that seeks to reuse features by concatenating them to new layers, allowing more information to be retained from previous layers of the network. This contrasts with say, residual connections, where element-wise summation is used instead to incorporate information from previous layers. This type of skip connection is prominently used in DenseNets (and also Inception networks), which the Figure to the right illustrates.
A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel. Source: Distilling the Knowledge in a Neural Network
Gaussian Processes are non-parametric models for approximating functions. They rely upon a measure of similarity between points (the kernel function) to predict the value for an unseen point from training data. The models are fully probabilistic so uncertainty bounds are baked in with the model. Image Source: Gaussian Processes for Machine Learning, C. E. Rasmussen & C. K. I. Williams
Stochastic Gradient Descent
Stochastic Gradient Descent is an iterative optimization technique that uses minibatches of data to form an expectation of the gradient, rather than the full gradient using all available data. That is for weights and a loss function we have: Where is a learning rate. SGD reduces redundancy compared to batch gradient descent - which recomputes gradients for similar examples before each parameter update - so it is usually much faster. (Image Source: here)
Discriminative Fine-Tuning is a fine-tuning strategy that is used for ULMFiT type models. Instead of using the same learning rate for all layers of the model, discriminative fine-tuning allows us to tune each layer with different learning rates. For context, the regular stochastic gradient descent (SGD) update of a model’s parameters at time step looks like the following (Ruder, 2016): where is the learning rate and is the gradient with regard to the model’s objective function. For discriminative fine-tuning, we split the parameters into {} where contains the parameters of the model at the -th layer and is the number of layers of the model. Similarly, we obtain {} where where is the learning rate of the -th layer. The SGD update with discriminative finetuning is then: The authors find that empirically it worked well to first choose the learning rate of the last layer by fine-tuning only the last layer and using as the learning rate for lower layers.
Logistic Regression, despite its name, is a linear model for classification rather than regression. Logistic regression is also known in the literature as logit regression, maximum-entropy classification (MaxEnt) or the log-linear classifier. In this model, the probabilities describing the possible outcomes of a single trial are modeled using a logistic function. Source: scikit-learn Image: Michaelg2015
Support Vector Machine
A Support Vector Machine, or SVM, is a non-parametric supervised learning model. For non-linear classification and regression, they utilise the kernel trick to map inputs to high-dimensional feature spaces. SVMs construct a hyper-plane or set of hyper-planes in a high or infinite dimensional space, which can be used for classification, regression or other tasks. Intuitively, a good separation is achieved by the hyper-plane that has the largest distance to the nearest training data points of any class (so-called functional margin), since in general the larger the margin the lower the generalization error of the classifier. The figure to the right shows the decision function for a linearly separable problem, with three samples on the margin boundaries, called “support vectors”. Source: scikit-learn
Linear Regression is a method for modelling a relationship between a dependent variable and independent variables. These models can be fit with numerous approaches. The most common is least squares, where we minimize the mean square error between the predicted values and actual values : . We can also define the problem in probabilistic terms as a generalized linear model (GLM) where the pdf is a Gaussian distribution, and then perform maximum likelihood estimation to estimate . Image Source: Wikipedia
Feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction.
A Feedforward Network, or a Multilayer Perceptron (MLP), is a neural network with solely densely connected layers. This is the classic neural network architecture of the literature. It consists of inputs passed through units (of which there can be many layers) to predict a target . Activation functions are generally chosen to be non-linear to allow for flexible functional approximation. Image Source: Deep Learning, Goodfellow et al
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Train a convolutional neural network to generate the contents of an arbitrary image region conditioned on its surroundings.
ADaptive gradient method with the OPTimal convergence rate
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A Gated Linear Unit, or GLU computes: It is used in natural language processing architectures, for example the Gated CNN, because here is the gate that control what information from is passed up to the following layer. Intuitively, for a language modeling task, the gating mechanism allows selection of words or features that are important for predicting the next word. The GLU also has non-linear capabilities, but has a linear path for the gradient so diminishes the vanishing gradient problem.
k-Means Clustering is a clustering algorithm that divides a training set into different clusters of examples that are near each other. It works by initializing different centroids {} to different values, then alternating between two steps until convergence: (i) each training example is assigned to cluster where is the index of the nearest centroid (ii) each centroid is updated to the mean of all training examples assigned to cluster . Text Source: Deep Learning, Goodfellow et al Image Source: scikit-learn
Normalizing Flows are a method for constructing complex distributions by transforming a probability density through a series of invertible mappings. By repeatedly applying the rule for change of variables, the initial density ‘flows’ through the sequence of invertible mappings. At the end of this sequence we obtain a valid probability distribution and hence this type of flow is referred to as a normalizing flow. In the case of finite flows, the basic rule for the transformation of densities considers an invertible, smooth mapping with inverse , i.e. the composition . If we use this mapping to transform a random variable with distribution , the resulting random variable has a distribution: where the last equality can be seen by applying the chain rule (inverse function theorem) and is a property of Jacobians of invertible functions. We can construct arbitrarily complex densities by composing several simple maps and successively applying the above equation. The density obtained by successively transforming a random variable with distribution through a chain of transformations is: The path traversed by the random variables with initial distribution is called the flow and the path formed by the successive distributions is a normalizing flow.
Adafactor is a stochastic optimization method based on Adam that reduces memory usage while retaining the empirical benefits of adaptivity. This is achieved through maintaining a factored representation of the squared gradient accumulator across training steps. Specifically, by tracking moving averages of the row and column sums of the squared gradients for matrix-valued variables, we are able to reconstruct a low-rank approximation of the exponentially smoothed accumulator at each training step that is optimal with respect to the generalized Kullback-Leibler divergence. For an matrix, this reduces the memory requirements from to . Instead of defining the optimization algorithm in terms of absolute step sizes {}, the authors define the optimization algorithm in terms of relative step sizes {}, which get multiplied by the scale of the parameters. The scale of a parameter vector or matrix is defined as the root-mean-square of its components, lower-bounded by a small constant . The reason for this lower bound is to allow zero-initialized parameters to escape 0. Proposed hyperparameters are: , , , , .
Masked autoencoder
Inverse Square Root is a learning rate schedule 1 / where is the current training iteration and is the number of warm-up steps. This sets a constant learning rate for the first steps, then exponentially decays the learning rate until pre-training is over.
Bidirectional LSTM
A Bidirectional LSTM, or biLSTM, is a sequence processing model that consists of two LSTMs: one taking the input in a forward direction, and the other in a backwards direction. BiLSTMs effectively increase the amount of information available to the network, improving the context available to the algorithm (e.g. knowing what words immediately follow and precede a word in a sentence). Image Source: Modelling Radiological Language with Bidirectional Long Short-Term Memory Networks, Cornegruta et al
Instance Normalization (also known as contrast normalization) is a normalization layer where: This prevents instance-specific mean and covariance shift simplifying the learning process. Intuitively, the normalization process allows to remove instance-specific contrast information from the content image in a task like image stylization, which simplifies generation.
RMSProp is an unpublished adaptive learning rate optimizer proposed by Geoff Hinton. The motivation is that the magnitude of gradients can differ for different weights, and can change during learning, making it hard to choose a single global learning rate. RMSProp tackles this by keeping a moving average of the squared gradient and adjusting the weight updates by this magnitude. The gradient updates are performed as: Hinton suggests , with a good default for as . Image: Alec Radford
RINLINEMATH1 Regularization is a regularization technique and gradient penalty for training generative adversarial networks. It penalizes the discriminator from deviating from the Nash Equilibrium via penalizing the gradient on real data alone: when the generator distribution produces the true data distribution and the discriminator is equal to 0 on the data manifold, the gradient penalty ensures that the discriminator cannot create a non-zero gradient orthogonal to the data manifold without suffering a loss in the GAN game. This leads to the following regularization term:
Spectral clustering has attracted increasing attention due to the promising ability in dealing with nonlinearly separable datasets [15], [16]. In spectral clustering, the spectrum of the graph Laplacian is used to reveal the cluster structure. The spectral clustering algorithm mainly consists of two steps: 1) constructs the low dimensional embedded representation of the data based on the eigenvectors of the graph Laplacian, 2) applies k-means on the constructed low dimensional data to obtain the clustering result. Thus,
A Dense Block is a module used in convolutional neural networks that connects all layers (with matching feature-map sizes) directly with each other. It was originally proposed as part of the DenseNet architecture. To preserve the feed-forward nature, each layer obtains additional inputs from all preceding layers and passes on its own feature-maps to all subsequent layers. In contrast to ResNets, we never combine features through summation before they are passed into a layer; instead, we combine features by concatenating them. Hence, the layer has inputs, consisting of the feature-maps of all preceding convolutional blocks. Its own feature-maps are passed on to all subsequent layers. This introduces connections in an -layer network, instead of just , as in traditional architectures: "dense connectivity".
Early Stopping is a regularization technique for deep neural networks that stops training when parameter updates no longer begin to yield improves on a validation set. In essence, we store and update the current best parameters during training, and when parameter updates no longer yield an improvement (after a set number of iterations) we stop training and use the last best parameters. It works as a regularizer by restricting the optimization procedure to a smaller volume of parameter space. Image Source: Ramazan Gençay
Conditional Random Field
Conditional Random Fields or CRFs are a type of probabilistic graph model that take neighboring sample context into account for tasks like classification. Prediction is modeled as a graphical model, which implements dependencies between the predictions. Graph choice depends on the application, for example linear chain CRFs are popular in natural language processing, whereas in image-based tasks, the graph would connect to neighboring locations in an image to enforce that they have similar predictions. Image Credit: Charles Sutton and Andrew McCallum, An Introduction to Conditional Random Fields
Stochastic Depth aims to shrink the depth of a network during training, while keeping it unchanged during testing. This is achieved by randomly dropping entire ResBlocks during training and bypassing their transformations through skip connections. Let {} denote a Bernoulli random variable, which indicates whether the th ResBlock is active () or inactive (). Further, let us denote the “survival” probability of ResBlock as . With this definition we can bypass the th ResBlock by multiplying its function with and we extend the update rule to: If , this reduces to the original ResNet update and this ResBlock remains unchanged. If , the ResBlock reduces to the identity function, .
A Focal Loss function addresses class imbalance during training in tasks like object detection. Focal loss applies a modulating term to the cross entropy loss in order to focus learning on hard misclassified examples. It is a dynamically scaled cross entropy loss, where the scaling factor decays to zero as confidence in the correct class increases. Intuitively, this scaling factor can automatically down-weight the contribution of easy examples during training and rapidly focus the model on hard examples. Formally, the Focal Loss adds a factor to the standard cross entropy criterion. Setting reduces the relative loss for well-classified examples (), putting more focus on hard, misclassified examples. Here there is tunable focusing parameter .
Linear Discriminant Analysis
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition, and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification. Extracted from Wikipedia Source: Paper: Linear Discriminant Analysis: A Detailed Tutorial Public version: Linear Discriminant Analysis: A Detailed Tutorial
Cycle Consistency Loss is a type of loss used for generative adversarial networks that performs unpaired image-to-image translation. It was introduced with the CycleGAN architecture. For two domains and , we want to learn a mapping and . We want to enforce the intuition that these mappings should be reverses of each other and that both mappings should be bijections. Cycle Consistency Loss encourages and . It reduces the space of possible mapping functions by enforcing forward and backwards consistency: