Deep learning MindMap

Concepts
Unit (Neurons)
A unit often refers to the activation
function in a layer by which the
inputs are transformed via a
nonlinear activation function (for
example by the logistic sigmoid
function). Usually, a unit has
several incoming connections and
several outgoing connections.
Input Layer
Comprised of multiple Real-Valued inputs. Each input
must be linearly independent from each other.
Hidden Layers
Layers other than the input and
output layers. A layer is the
highest-level building block in
deep learning. A layer is a
container that usually receives
weighted input, transforms it with
a set of mostly non-linear
functions and then passes these
values as output to the next
layer.
Batch Normalization
Using mini-batches of examples, as opposed to one example at a time, is helpful in
several ways. First, the gradient of the loss over a mini-batch is an estimate of the
gradient over the training set, whose quality improves as the batch size increases.
Second, computation over a batch can be much more efficient than m computations for
individual examples, due to the parallelism afforded by the modern computing platforms.
With SGD, the training proceeds in steps, and
at each step we consider a mini- batch x1...m
of size m. The mini-batch is used to approx-
imate the gradient of the loss function with
respect to the parameters.
Cost/Loss(Min)
Objective(Max)
Functions
Maximum
Likelihood
Estimation (MLE)
Many cost functions are the result of applying Maximum Likelihood. For instance, the Least Squares
cost function can be obtained via Maximum Likelihood. Cross-Entropy is another example.
The likelihood of a parameter value (or vector of parameter values), θ,
given outcomes x, is equal to the probability (density) assumed for those
observed outcomes given those parameter values, that is
The natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with. Because the
logarithm is a monotonically increasing function, the logarithm of a function achieves its maximum value at the same
points as the function itself, and hence the log-likelihood can be used in place of the likelihood in maximum likelihood
estimation and related techniques.
In general, for a fixed set of data and underlying
statistical model, the method of maximum likelihood
selects the set of values of the model parameters that
maximizes the likelihood function. Intuitively, this
maximizes the "agreement" of the selected model with
the observed data, and for discrete random variables it
indeed maximizes the probability of the observed data
under the resulting distribution. Maximum-likelihood
estimation gives a unified approach to estimation,
which is well-defined in the case of the normal
distribution and many other problems.
Cross-Entropy
Cross entropy can be used to define the loss
function in machine learning and optimization.
The true probability pi is the true label, and
the given distribution qi is the predicted value
of the current model.
Cross-entropy error function and logistic regression
Logistic The logistic loss function is defined as:
Quadratic
The use of a quadratic loss function is common, for example when
using least squares techniques. It is often more mathematically
tractable than other loss functions because of the properties of
variances, as well as being symmetric: an error above the target
causes the same loss as the same magnitude of error below the target.
If the target is t, then a quadratic loss function is:
0-1 Loss
In statistics and decision theory, a frequently
used loss function is the 0-1 loss function
Hinge Loss
The hinge loss is a loss function used for
training classifiers. For an intended output t =
±1 and a classifier score y, the hinge loss of
the prediction y is defined as:
Exponential
Hellinger Distance
It is used to quantify the similarity between
two probability distributions. It is a type of f-
divergence.
To define the Hellinger distance in terms of
measure theory, let P and Q denote two
probability measures that are absolutely
continuous with respect to a third probability
measure λ. The square of the Hellinger
distance between P and Q is defined as the
quantity
Kullback-Leibler Divengence
Is a measure of how one probability
distribution diverges from a second expected
probability distribution. Applications include
characterizing the relative (Shannon) entropy
in information systems, randomness in
continuous time-series, and information gain
when comparing statistical models of
inference.
Discrete Continuous
Itakura–Saito distance
is a measure of the difference between an
original spectrum P(ω) and an approximation
P^(ω) of that spectrum. Although it is not a
perceptual measure, it is intended to reflect
perceptual (dis)similarity.
https://stats.stackexchange.com/questions/154879/a-list-of-cost-functions-used-in-neural-networks-alongside-applications
https://en.wikipedia.org/wiki/Loss_functions_for_classification
Regularization
L1 norm Manhattan Distance
L1-norm is also known as least absolute
deviations (LAD), least absolute errors (LAE). It
is basically minimizing the sum of the
absolute differences (S) between the target
value and the estimated values.
L2 norm Euclidean Distance
L2-norm is also known as least squares. It is
basically minimizing the sum of the square of
the differences (S) between the target value
and the estimated values:
Early Stopping
Early stopping rules provide guidance as to how many iterations can be
run before the learner begins to over-fit, and stop the algorithm then.
Dropout
Is a regularization technique for reducing overfitting in neural networks by preventing
complex co-adaptations on training data. It is a very efficient way of performing model
averaging with neural networks. The term "dropout" refers to dropping out units (both
hidden and visible) in a neural network
Sparse regularizer on columns
This regularizer defines an L2 norm on each
column and an L1 norm over all columns. It
can be solved by proximal methods.
Nuclear norm regularization
Mean-constrained regularization
This regularizer constrains the functions learned for each task to be similar to
the overall average of the functions across all tasks. This is useful for
expressing prior information that each task is expected to share similarities
with each other task. An example is predicting blood iron levels measured at
different times of the day, where each task represents a different person.
Clustered mean-constrained regularization
This regularizer is similar to the mean-
constrained regularizer, but instead enforces
similarity between tasks within the same
cluster. This can capture more complex prior
information. This technique has been used to
predict Netflix recommendations.
Graph-based similarity
More general than above, similarity between
tasks can be defined by a function. The
regularizer encourages the model to learn
similar functions for similar tasks.
Weight Initialization
All Zero Initialization
In the ideal situation, with proper data
normalization it is reasonable to assume that
approximately half of the weights will be
positive and half of them will be negative. A
reasonable-sounding idea then might be to
set all the initial weights to zero, which you
expect to be the “best guess” in expectation.
But, this turns out to be a mistake, because if
every neuron in the network computes the
same output, then they will also all compute
the same gradients during back-propagation
and undergo the exact same parameter
updates. In other words, there is no source of
asymmetry between neurons if their weights
are initialized to be the same.
Initialization with Small Random Numbers
Thus, you still want the weights to be very
close to zero, but not identically zero. In this
way, you can random these neurons to small
numbers which are very close to zero, and it is
treated as symmetry breaking. The idea is that
the neurons are all random and unique in the
beginning, so they will compute distinct
updates and integrate themselves as diverse
parts of the full network.
The implementation for weights might simply
drawing values from a normal distribution with
zero mean, and unit standard deviation. It is
also possible to use small numbers drawn
from a uniform distribution, but this seems to
have relatively little impact on the final
performance in practice.
Calibrating the Variances
One problem with the above suggestion is
that the distribution of the outputs from a
randomly initialized neuron has a variance that
grows with the number of inputs. It turns out
that you can normalize the variance of each
neuron's output to 1 by scaling its weight
vector by the square root of its fan-in (i.e., its
number of inputs)
This ensures that all neurons in the network
initially have approximately the same output
distribution and empirically improves the rate
of convergence. The detailed derivations can
be found from Page. 18 to 23 of the slides.
Please note that, in the derivations, it does
not consider the influence of ReLU neurons.
Optimization
Gradient Descent
Is a first-order iterative optimization algorithm for finding the minimum of a function. To find a
local minimum of a function using gradient descent, one takes steps proportional to the
negative of the gradient (or of the approximate gradient) of the function at the current point. If
instead one takes steps proportional to the positive of the gradient, one approaches a local
maximum of that function; the procedure is then known as gradient ascent.
Stochastic Gradient Descent (SGD)
Gradient descent uses total gradient over all
examples per update, SGD updates after only
1 or few examples:
Mini-batch Stochastic Gradient Descent
(SGD)
1 example
Momentum
Idea: Add a fraction v of previous update to
current one. When the gradient keeps pointing
in the same direction, this will
increase the size of the steps taken towards
the minimum.
AdagradAdaptive learning rates for each parameter
Learning Rate
Neural networks are often trained by gradient
descent on the weights. This means at each
iteration we use backpropagation to calculate
the derivative of the loss function with respect
to each weight and subtract it from that
weight.
However, if you actually try that, the weights
will change far too much each iteration, which
will make them “overcorrect” and the loss will
actually increase/diverge. So in practice,
people usually multiply each derivative by a
small value called the “learning rate” before
they subtract it from its corresponding weight.
Tricks
Simplest recipe: keep it fixed and use the
same for all parameters.
Better results by allowing learning rates to decrease Options:
Reduce by 0.5 when validation error stops improving
Reduction by O(1/t) because of theoretical
convergence guarantees, with hyper-
parameters ε0 and τ and t is iteration
numbers.
Better yet: No hand-set learning of rates by using AdaGrad
Backpropagation
Is a method used in artificial neural networks to
calculate the error contribution of each neuron
after a batch of data. It calculates the gradient
of the loss function. It is commonly used in the
gradient descent optimization algorithm. It is
also called backward propagation of errors,
because the error is calculated at the output
and distributed back through the network
layers.Neural Network taking 4 dimension vector
representation of words.
In this method, we reuse partial derivatives
computed for higher layers in lower layers, for
efficiency.
Intuition for backpropagation
Simple Example (Circuits)Another Example (Circuits)
Simple Example (Flowgraphs)
Activation Functions
Defines the output of that node given an input
or set of inputs.
Types
ReLU
Sigmoid / Logistic
Binary
Tanh
Softplus
Softmax
Maxout
Leaky ReLU, PReLU, RReLU, ELU, SELU, and others.

Architectures Strategy
1. Select Network Structure appropriate for
problem
Structure: Single words, fixed windows,
sentence based, document level; bag of
words, recursive vs. recurrent, CNN
Nonlinearity (Activation Functions)
2. Check for implementation bugs with
gradient checks
1. Implement your gradient
2. Implement a finite difference computation
by looping through the parameters of your
network, adding and subtracting a small
epsilon ( 10-4) and estimate derivatives
3. Compare the two and make sure they are
almost the same
Using Gradient Checks
If you gradient fails and you don’t know why?
Simplify your model until you have no bug!
What now? Create a very tiny synthetic model
and dataset
Example: Start from simplest model then go
to what you want:
Only softmax on fixed input
Backprop into word vectors and softmax
Add single unit single hidden layer
Add multi unit single layer
Add second layer single unit, add multiple
units, bias • Add one softmax on top, then
two softmax layers
Add bias
3. Parameter initialization
Initialize hidden layer biases to 0 and output
(or reconstruction) biases to optimal value if
weights were 0 (e.g., mean target or inverse
sigmoid of mean target).
Initialize weights Uniform(−r, r), r inversely
proportional to fan-in (previous layer size) and
fan-out (next layer size):
4. Optimization
Gradient Descent
Is a first-order iterative optimization algorithm for finding the minimum of a function. To find a
local minimum of a function using gradient descent, one takes steps proportional to the
negative of the gradient (or of the approximate gradient) of the function at the current point. If
instead one takes steps proportional to the positive of the gradient, one approaches a local
maximum of that function; the procedure is then known as gradient ascent.
Stochastic Gradient Descent (SGD)
1 or few examples:
Ordinary gradient descent as a batch method
is very slow, should never be used. Use 2nd
order batch method such as L-BFGS.
On large datasets, SGD usually wins over all
batch methods. On smaller datasets L-BFGS
or Conjugate Gradients win. Large-batch L-
BFGS extends the reach of L-BFGS [Le et al.
ICML 2011].
Mini-batch Stochastic Gradient Descent
(SGD)
1 example
Most commonly used now, Size of each mini
batch B: 20 to 1000
Helps parallelizing any model by computing
gradients for multiple elements of the batch in
parallel
Momentum
Idea: Add a fraction v of previous update to
current one. When the gradient keeps pointing
in the same direction, this will
increase the size of the steps taken towards
the minimum.
Reduce global learning rate when using a lot
of momentum
Update Rule
v is initialized at 0
Momentum often increased after some
epochs (0.5 à 0.99)
Adagrad
Adaptive learning rates for each parameter!
Learning rate is adapting differently for each
parameter and rare parameters get larger
updates than frequently occurring parameters.
Word vectors!
5. Check if the model is powerful enough to
overfit
If not, change model structure or make model “larger”
If you can overfit: Regularize to prevent
overfitting:
Simple first step: Reduce model size by
lowering number of units and layers and other
parameters
Standard L1 or L2 regularization on weights
Early Stopping: Use parameters that gave
best validation error
Sparsity constraints on hidden activations,
e.g., add to cost:
Dropout
Training time: at each instance of evaluation
(in online SGD-training), randomly set 50% of
the inputs to each neuron to 0
Test time: halve the model weights (now twice
as many) This prevents feature co-adaptation:
A feature cannot only be useful in the
presence of particular other features
In a single layer: A kind of middle-ground
between Naïve Bayes (where all feature
weights are set independently) and logistic
regression models (where weights are set in
the context of all others)
Can be thought of as a form of model bagging
It also acts as a strong regularizer
RNNs (Recursive)
Is a kind of deep neural
network created by applying
the same set of weights
recursively over a structure, to
produce a structured prediction
over variable-size input
structures, or a scalar
prediction on it, by traversing a
given structure in topological
order.
RNNs have been successful for instance in
learning sequence and tree structures in
natural language processing, mainly phrase
and sentence continuous representations
based on word embedding.
RNNs (Recurrent)
Is a class of artificial neural network where connections between units form a
directed cycle. This allows it to exhibit dynamic temporal behavior. Unlike
feedforward neural networks, RNNs can use their internal memory to process
arbitrary sequences of inputs.
This makes them applicable to tasks such as
unsegmented, connected handwriting recognition or
speech recognition.
Convolutional Neural Networks (CNN)
They have applications in image and video
recognition, recommender systems and
natural language processing.
Pooling
Convolution
Subsampling
Auto-Encoders
Is an artificial neural network used for unsupervised
learning of efficient codings.
The aim of an autoencoder
is to learn a representation
(encoding) for a set of data,
typically for the purpose of
dimensionality reduction.
Recently, the autoencoder
concept has become more
widely used for learning
generative models of data.
GANs
GANs or Generative
Adversarial Networks are a
class of artificial intelligence
algorithms used in
unsupervised machine
learning, implemented by a
system of two neural networks
contesting with each other in a
zero-sum game framework.
LSTMs
Long short-term memory - It is a type of recurrent (RNN), allowing
data to flow both forwards and backwards within the network.
An LSTM is well-suited to learn from
experience to classify, process and predict
time series given time lags of unknown size
and bound between important events.
Relative insensitivity to gap length gives an
advantage to LSTM over alternative RNNs,
hidden Markov models and other sequence
learning methods in numerous applications.
Feed Forward
Is an artificial neural network wherein connections between the units do not form a
cycle. In this network, the information moves in only one direction, forward, from the
input nodes, through the hidden nodes (if any) and to the output nodes. There are no
cycles or loops in the network.
Kinds
Single-Layer Perceptron
The inputs are fed directly to the outputs via a
series of weights. By adding an Logistic
activation function to the outputs, the model
is identical to a classical Logistic Regression
model.
Multi-Layer Perceptron
This class of networks consists of multiple
layers of computational units, usually
interconnected in a feed-forward way. Each
neuron in one layer has directed connections
to the neurons of the subsequent layer. In
many applications the units of these networks
apply a sigmoid function as an activation
function.

Tensorflow
Packages
tf Main Steps
1. Create the Model
2. Define Target
3. Define Loss function and Optimizer
4. Define the Session and Initialise Variables
5. Train the Model
6. Test Trained Model
tf.estimator
TensorFlow’s high-level machine learning API
(tf.estimator) makes it easy to configure, train, and
evaluate a variety of machine learning models.
tf.estimator.LinearClassifier: Constructs a linear classification model.
tf.estimator.LinearRegressor: Constructs a linear regression model.
tf.estimator.DNNClassifier: Construct a neural network classification model.
tf.estimator.DNNRegressor: Construct a neural network regression model.
tf.estimator.DNNLinearCombinedClassifier: Construct a neural network and linear combined classification model.
tf.estimator.DNNRegressor: Construct a neural network and linear combined regression model.
Main Steps
1. Define Feature Columns
FeatureColumns are the primary way of
encoding features for pre-canned tf.learn
Estimators.
Categorical Numerical
When using FeatureColumns with tf.learn
models, the type of feature column you
should choose depends on the feature type
and the model type.
Continuous Features Can be represented by real_valued_column
Categorical Features
Can be represented by any
sparse_column_with_* column
(sparse_column_with_keys,
sparse_column_with_vocabulary_file,
sparse_column_with_hash_bucket,
sparse_column_with_integerized_feature
2. Define your Layers, or use a prebuilt model
Using a pre-built Logistic Regression
Classifier
3. Write the input_fn function
This function holds the actual data (features
and labels). Features is a python dictionary.
4. Train the model
Using the fit function, on the input_fn. Notice
that the feature columns are fed to the model
as arguments.
5. Predict and Evaluate Using the eval_input_fn defined previously.
Comparison to Numpy
Does lazy evaluation. Need to build the
graph, and then run it in a session.
Main Components
Variables
Stateful nodes that output their current value,
their state is retained across multiple
executions of the graph.
Mostly Parameters we’re interested in tuning,
such as Weights (W) and Biases (b).
Sharing
Variables can be shared by Explicitly passing
tf.Variable objects around, or...
Implicitly wrapping tf.Variable objects within
tf.variable_scope objects.
Scopes
tf.variable_scope()
Provides simple name spacing to avoid cases
when querying
tf.get_variable()
Creates/Access variables from a variable
scope
Placeholders
Nodes whose value is fed at execution time.
Inputs, Features (X) and Labels (y)
Mathematical
Operations
MatMul, Add, ReLU, etc.
Graph
Nodes
They are Operations, containing any number
of inputs and outputs.
EdgesThe tensors that flow between the nodes.
Session
It a binding to a particular execution context: CPU, GPU.
Running a SessionInputs
Fetches
List of graph nodes. Returns the output of
these nodes.
Feeds
Dictionary mapping from graph nodes to
concrete values.
Specified the value of each graph node given
in the dictionary.
Phases
1. Construction
Assembles a computational graph
The computation graph has no numerical
value until evaluated.
All computations add nodes to global default graph
2. Execution
A Session object encapsulates the environment
in which Tensor objects are evaluated
Uses a session to execute ops in the graph
Declared variables must be initialised before
they have values.
When you train a model you use variables to hold and update
parameters. Variables are in-memory buffers containing tensors.
TensorboardTensorFlow has some neat built-in visualization tools (TensorBoard).
Intuition
TensorFlow is a deep learning library recently open-sourced by
Google. It provides primitives for defining functions on tensors and
automatically computing their derivatives, expressed as a graph.
The Tensorflow Graph is build to contain all placeholders for X and y,
all variables for W’s and b’s, all mathematical operations, the cost
function, and the optimisation procedure. Then, at runtime, the values
for the data are fed into that Graph, by placing the data batches in
the placeholders and running the Graph.
Each node in the Graph can then be connected to each other node
over the network, and thus running Tensorflow models can be
parallelised.

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