Data structures and applicability

Lists

Sets – Doesn’t maintain order and doesn’t allow repeated elements.

Stacks – Depth-first search, behave similar to recursion and can be a replacement for it.

Queues – Breadth-first search

Heaps – (Priority queue)

  1. Supports
    1. Insertion – O(logn)
    2. Extract min/max – O(logn)
    3. Heapify – O(n)
    4. Delete – O(logn)
  2. Applications:
    1. Scheduled event managing.
    2. Median maintenance – using two heaps, one max heap, and one min heap.
    3. Dijkstra Algorithm – O(m log n)

Search trees –

Trees :

  1. All the nodes should be connected.
  2. should not have cycles.

 

  1. Balanced binary search trees:
    1. Red-black trees.
    2. AVL trees.
    3. Splay trees.

Hash tables –

  1. When you don’t need to remember ordering, minimum or maximum.
  2. To check whether an element exists – O(1)
  3. Insertions and deletions – O(1)
  4. Applications:
    1. 2-sum problem.
  5. Hash function:
  6. Resolving collisions:
    1. Chaining: Linked lists inside each bucket.
    2. open addressing (probe sequence) – one object per bucket.
  7. Choose num of buckets as a prime number.
  8. Load factor: Num of objects/ Num of buckets.
  9. Every hash function has a pathological data set.
  10. Randomization from a family of hash functions at runtime.

Hashing – Use a hash function which deduces the index in which to store the value based on the digits of the value itself (usually last few digits). Store the value in the provided index. when you want to lookup, it is of O(1), since lookup from an indexed array is of constant time.

Bloom filters –

  1. More space efficient than hash tables.
  2. No deletions.
  3. Small false positive probability – might say x has been inserted even though it hasn’t been.
  4. Operations:
    1. Fast inserts and lookups.
  5. Applications:
    1. Spell-checker.
    2. List of forbidden passwords.
    3. Network routers – Limited memory, need to be super fast.

 

 

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Tensorflow Speech Recognition challenge

 

  1. Definition

Project Overview

The project is closely related to Automatic Speech Recognition except that instead of recognizing the continuous speech constituting of many different words and sentences, we will be recognizing a small set of words and label remaining as unknown or silence. The training and test data contains wave files of nearly one second long each one uttering a word, noise or just silence.

The datasets required to train this project are provided by Google as part of a kaggle speech recognition challenge (kaggle).

In the age all digital products attempting to communicate with their customers in terms of speech rather than typing, ASR and NLP have been an interesting as well as important field of study. You can find brief history of research in the field of ASR in this link.

Problem Statement

The problem is to classify all the sound wave files into twelve broad categories of [‘down’, ‘go’, ‘left’, ‘no’, ‘off’, ‘on’, ‘right’, ‘stop’, ‘up’, ‘yes’, ‘unknown’, ‘silence’]

To achieve this,

  1. We will classify whether a wave file has any voice or it is just a silent file.
  2. For all the non-silent files, we will build a model that can classify whether the sound in the wave file belongs to one of the words mentioned above or some unknown word or sound.
  3. The anticipated solution/ model should predict all the 12 categories as accurately as possible in a large sample test set.

Metrics

Kaggle provides a test set of nearly 150000 samples of wave files for which I will predict the labels and create a submission file to submit. Kaggle will provide the accuracy of my predictions based on the submission file.

Apart from this, we will do test train split of training data and check our models performance on training and test data samples with train and validation accuracies.

Since this is a classification problem with a few set of specific labels possible, accuracy is a good metric to gauge our model as we are only concerned about getting the prediction exactly right or wrong and all classes are equally important.

  1. Analysis

Data Exploration

Our training set contains .wav files with variants of 30 class labels, where each class label is a word. Number of training .wav files provided for each wave is around 2000 on average which is large enough for training a good model. Out of the approximate 64000 .wav files, nearly 4000 files were detected by VAD (Voice Activation Detector) as silent or noise files. We have excluded these from training set. Few of the word pairs in the dataset like (go, no) etc. have very close pronunciation and predictions compete closely with each other as well. Each wave had some silence/noise padded before and after the word for which we had to use VAD and strip off frames of that sort. One such wave for example is provided in Exploratory Visualization section.

 

Initially we assumed that for some words in test set that are other than these 30 words (among which we have to recognize 10 words as is and other twenty as unknown), the model will probably not return probabilities more than the threshold for any of the labels and hence we can consider that word as unknown. However, since it is hard to find proper threshold of that kind even if that exists, we introduced a new label called “Unknown unknowns” which are some words apart from these 30. It is probably tough for the model to converge all other words with varied features to aggregate as single class. We also need to prepare some test data with random words to this Unknown unknown’s class.  The procedure we followed to create data for Unknown unknown’s class is: 1.     Take a wave file from existing training set and find the max amplitude index from that wave’s samples.2.     Take the wave from beginning to that max sample value and store it as first half of the final wave required.3.     Take another random wave and pick max sample value to end samples to create second half of the final wave.4.     Merge first half and second half to get a new wave file with some random sound which might not even be an actual word.5.     This data will be a right fit for the unknown unknown’s class.

 

Exploratory Visualization

Plot of raw wave and its spectrogram:

 

Plot of sample MFCC for a wave file:

 

 

[i]We have plotted mean fft and spectrogram of different words that needs to be classified, to decide on which features to pick for classification.

 

Then we did violin plot to identify amount of different frequencies in each word label of training set.

 

Algorithms and Techniques

Since speech is a time series where sentences are sequences of words and words are sequences of phonemes, we chose long short term memory networks which can hold the memory of recent phonemes and predict the next phoneme considering the memory and subsequently word.

 

Though we could have tackled this problem using convolutional neural network, since the problem is restricted to words, eventually when we need to scale it to sentences, it makes sense to approach with LSTM. Though RNNs are good for sequential data, when you need to predict long term dependencies, it is better to use LSTMs over vanilla RNN. LSTMs remember data for longer periods of time comparatively.

 

A standard LSTM cell consists of:

  1. A forget layer which makes the decision what needs to be remembered and passed from previous cell state and what needs to be forgotten.
  2. An input gate layer which makes the decision of what part of input needs to be added to the cell state.
  3. An output gate layer which decides which part of cell state should be given as output.

A slightly modified version of the same called Gated Recurrent unit.

 

 

We chose binary cross-entropy and categorical accuracy to train our model as it is a Multi-classification problem to predict our labels. Our labels are one-hot encoded and passed on to model for training.

 

We have probabilities for each label coming out of the model and picked the label with maximum probability after passing through a threshold value. If none of the labels is more than the threshold, we guessed the word as unknown.

 

For silence labels, we have passed the wave through the VAD even before passing it model for prediction and labelled accordingly.

 

The model will be given an input numpy array of size (16, 26) which will be taken by an input LSTM layer where 16 represents sequence of 16 frames and 26 represents the mfcc and delta_mfcc features of each frame.

 

Benchmark

I have picked the results of my first trained model as the benchmark which contained 12 labels with a dense layer at the output, one LSTM input layer and one LSTM hidden layer. The accuracy of that model against the test set was 0.62.

 

Test accuracy: 0.62

 

Layer (type)                 Output Shape              Param #

=================================================================

lstm_1 (LSTM)                (None, 16, 39)            8268

_________________________________________________________________

lstm_2 (LSTM)                (None, 26)                6864

_________________________________________________________________

dense_1 (Dense)              (None, 12)                810

=================================================================

Total params: 15,942

Trainable params: 15,942

Non-trainable params: 0

 

III. Methodology

Data Preprocessing

After considering, spectrogram, fft and mfcc for Features to train a model, We chose to build features based on mel scale, which is inspired by how humans process speech in ears. Hence built mfcc features for each wave which is stripped off with silence using Voice Activation Detection.

 

We have used Librosa library to build mfcc features from a raw sound wave. It includes

 

  1. Converting wave file into smaller frames.
  2. Find the power spectrum of each frame
  3. Apply mel filter bank to the spectra and sum power inside each filter.
  4. Take logarithm of few filterbank energies.
  5. Convert them to DCT and pick few important coefficients of the same.

 

These coefficients are called Mel-frequency cepstral coefficients and state of the art in Automatic Speech Recognition systems.

 

Later on, considering Speech information could be present in dynamics of spectral frames, rather than just the spectral envelope of frames, we added delta mfcc features as well.

 

Stacking both mfcc and delta_mfcc features for each frame and doing it for all 16 frames of the wave, we have ended up with features of size (16, 26).

Implementation

Machine Learning Pipeline: 1.     Pass wave file through VAD (Voice Activity Detector) to filter out and label all silence files.2.     Pass remaining wave files through chosen feature extractor, MFCCs in this case.3.     Pass the features through stacked LSTM model which can detect patterns across long range of phonemes/frames in the wave file and has the output of 32 labels.4.     Train the model with different parameters with epochs enough for the model to converge. It took around 30 minutes to train each epoch in my CPU and the model used to take around 15 to 20 epochs to converge. It is very time consuming to experiment each time to train the model.   _________________________________________________________________Layer (type)                 Output Shape              Param #   =================================================================lstm_9 (LSTM)                (None, 16, 52)            16432     _________________________________________________________________dropout_9 (Dropout)          (None, 16, 52)            0         _________________________________________________________________lstm_10 (LSTM)               (None, 16, 45)            17640     _________________________________________________________________dropout_10 (Dropout)         (None, 16, 45)            0         _________________________________________________________________lstm_11 (LSTM)               (None, 45)                16380     _________________________________________________________________dense_5 (Dense)              (None, 45)                2070      _________________________________________________________________dropout_11 (Dropout)         (None, 45)                0         _________________________________________________________________dense_6 (Dense)              (None, 30)                1380      =================================================================Total params: 53,902Trainable params: 53,902Non-trainable params: 0_________________________________________________________________

Refinement

 

The initial solution had our model with 11 labels, with two LSTM layers and one dense output layer. It had only mfcc features and delta_mfcc were added later. All the words other than the ten words that needs to be predicted are grouped and one label.

 

Accuracy on test set : 0.63

 

Layer (type)                 Output Shape              Param #

=================================================================

lstm_1 (LSTM)                (None, 16, 39)            8268

_________________________________________________________________

lstm_2 (LSTM)                (None, 26)                6864

_________________________________________________________________

dense_1 (Dense)              (None, 11)                810

=================================================================

Total params: 15,942

Trainable params: 15,942

Non-trainable params: 0

 

 

Then, we have added delta features, drop out layers for regularization to avoid overfitting. We have changed the number of labels in the output dense layer to 31. This increased the number of trainable parameters to approximately 53k and significantly increased the model training time per epoch.

Initially we were working with threshold value of 0.5, which skipped many words that are recognized around 0.25 and 0.3 max probabilities. After reducing threshold to 0.1, score has crossed 0.7 on the leaderboard test set.

 

Later on, I have split background noise wave files into multiple 1 sec long waves and used them as well as training data for another model has one more silence label included which makes it to a 32 labelled model.

Using the batch size parameter while fitting the model to training data helped regarding the training time.

Final model:

Layer (type)                 Output Shape              Param #

=================================================================

lstm_32 (LSTM)               (None, 16, 96)            41856

_________________________________________________________________

lstm_33 (LSTM)               (None, 16, 96)            74112

_________________________________________________________________

lstm_34 (LSTM)               (None, 96)                74112

_________________________________________________________________

dense_18 (Dense)             (None, 32)                3104

=================================================================

Total params: 193,184

Trainable params: 193,184

Non-trainable params: 0

 

 

  1. Results

Free Form Visualization:

As I’ve recorded the accuracy and loss of the models per epoch, here’s the accuracy/loss graph of the model with batch normalization.

 

As we can see the training accuracy is near 100% in the diagram and the loss is near 0. Similarly the validation accuracy is also near 95% while the validation loss is around 0.2% near the end of the 30 epochs. We also see the trend where the validation loss reached the lower bound before the training loss. Clearly this model is overfitting on the training data.

Model Evaluation and Validation

 

The final model has been tested against the test set of 1.5 lakh samples with varied sounds including normal words, meaningless sounds, different kinds of noises, silence samples etc.  Hence the score on the test set validates the model to be of reasonably good quality.

Our model is robust enough as we take the sound wave through Voice Activity Detection and strip off the sound wave from unwanted silent frames and pass on only the valid sound frames to the model for prediction. I have created some wave files with words spoken in the different background noises and model was robust enough to predict the words.

I have also hand-picked few predictions from the test set and verified manually to validate my model’s predictions.

The final model has reported an accuracy of 0.75 in test set of 1.5 lakh samples and close to 0.95 on training set.

Justification

The accuracy of 0.75 on test set produced by the final model is lot better than the 0.63 score of initial benchmark model.

The final solution had stacked LSTM of three layers, first two returning full sequences while the last layer returns a vector.  These layers are followed by dense layers of 32 nodes equivalent to number of labels to predict.

Though it has lot of scope for improvement and experimentation which is described in below section, this score and model is robust and significant enough to do speech recognition for specified labels.

  1. Conclusion

Reflection

After trying out with different models and feature data, the best model obtained has the unknown unknowns (words not in training set considered) and have been trained on 32 labels with MFCC features. One more binary classification for detecting Silence in the wave file is employed. We have stripped off silent frames in the audio file before training. Model with LSTM layers considering sequences and memory states with dropout layers for generalization have been fruitful.

 

One difficult and yet interesting part of this problem is classifying words that pronounce closely and classifying words in dominating background noise which can possibly have multiple interpretations. For examples, go and no pronounce closely and can be easily mistaken in noisy background. However, even humans might not be accurate in this situations but the sentence context can have some information which hints towards a particular word in real word situations.

Improvement

  1. The dimensionality of features is huge and try using PCA to remove some dimensions of negligible variance before passing it to the model for training.
  2. Though the MFCC features are state of the art in speech recognition based on the literature, we should try other features like raw wave, fft, log mel features etc and combinations of different features as well.
  3. We should try using few other neural network layers for mfcc features and see how the model performs. Some of them might include:
    1. Convolution LSTM.
    2. Densenet201 etc.
  4. I should try other models like XGBoost (LGBM implementation, as it is computationally effective), random forest kind of ensemble models and see how they perform on this Multi-classification problem.
  5. I should either setup or rent GPU to run these models as these will take days if I were to run on normal CPU. I need to make use floydhub, paperspace or vectordash in future.
  6. I believe, experimenting all these options with proper computational power will definitely enhance my final benchmark model.
  7. Listen to mislabeled samples in validation set.
  8. Data augmentation: Add heavy noise augmentation while keeping noise vs signal ratio below 2.

[i]

 

References :

 

You can find data required for this project in below link https://www.kaggle.com/c/tensorflow-speech-recognition-challenge/data

Some of the Blog posts followed:

  1. https://ideasforeversite.wordpress.com/2018/03/18/automatic-speech-recognition/
  2. http://practicalcryptography.com/miscellaneous/machine-learning/guide-mel-frequency-cepstral-coefficients-mfccs/
  3. Voice Activity Detection : https://pypi.python.org/pypi/webrtcvad , https://github.com/wiseman/py-webrtcvad/blob/master/example.py

https://github.com/marsbroshok/VAD-python

https://github.com/marsbroshok/VAD-python/blob/master/detectVoiceInWave.py

Libraries used:

  1. For extracting MFCC features : https://librosa.github.io/librosa/generated/librosa.feature.mfcc.html
  2. Keras : https://keras.io/layers/recurrent/#lstm

Boiler plate: https://www.kaggle.com/davids1992/speech-representation-and-data-exploration

 

https://dsp.stackexchange.com/questions/13817/how-to-reduce-speech-feature-dimensions

 

 

HEAD FIRST DESIGN PATTERNS

 

  1. The code should be closed to change and open to extension, should be easily maintainable for future change requests.
  2. Prefer composition (change behavior in runtime, encapsulate family of algorithms) over inheritance (your behavior is stuck). (why?)
  3. All design patterns have pros and cons. The decision of whether I should use a design pattern in a situation should be taken after analyzing whether the product you are building can afford to have cons offered by the pattern.

Situation (when):

Design pattern solution (what): Class diagram

Pros and Cons (why):

Decorator pattern (follows open-closed principle):

Situation:

When there are a lot of combinations to deal with in different categories.

Normal solution (stupid way): Enumerate all the combinations possible and write a method in subclass specific to each combination.

Maintenance problems with this solution:

  1. If the price of milk goes up, they have to change the code in all the places.
  2. If they add a new item in one category, the whole thing explodes even more combinatorically.

One more solution:

Take Boolean instance variable for the presence of each specific condiment and deduce cost of the all condiments based on that in the parent class and you can add the cost of that specific beverage alone in the subclass and call super.cost().

Some problems with this solution:

  1. We have to alter existing code if there is a change in the price of any condiment.
  2. New condiments in future means, new instance variables, new setters and getters and we also need to modify the cost method in the superclass to account for this new condiment as well.
  3. Some of the beverage and condiment combinations may not be appropriate and we have no way of restricting them.
  4. What if the customer wants a double mocha?

Time for One more solution:

When inheriting behavior by sub-classing, the behavior is set statically at compile time.

Design pattern solution:

Inheriting behavior at runtime through composition and delegation. More flexibility.

If u want a Dark roast with condiments of mocha and whip, Take a dark roast object, decorate it with a mocha object and decorate it with the whip and call the cost function and rely on delegation.

Decorator objects are kind of wrappers.

The concrete decorator has an instance variable for the thing it decorates.

We can implement new decorators any time to add new behavior instead of changing existing code which is thoroughly tested.

Decorators are usually created by using Factory and Builder patterns.

Alternative to sub-classing for extending functionality.

Enables a lot of combinations with a minimal number of classes possible.

Demerits:

  1. Introduces complexity to the code and reduces readability.
  2. If you have some logic that is specific to a component type like the discount in this case, then this would not be applicable.
  3. You end up adding a lot of small classes.

Adapter pattern:

 

Facade Pattern:

Situation:

  1. To simplify the interface of a group of classes.

Iterator Pattern:

This along with composite pattern helps you deal with a collection of Objects better.

Situation:

  1. If you want to iterate across collectibles of varied types like ArrayList, Hashmap, etc, provided the component type remains same (check).
  2. To provide a way to access elements of an aggregate object sequentially without worrying about its underlying implementation.

Composite Pattern:

Situation:

  1. If you want to treat tree-like structures, leaf nodes, and composites uniformly.
  2. If you want your sub-categories to behave in the same way as your categories.
  3. The difference from iterator pattern is, here the component type itself varies.

Design pattern:

Looks familiar to Depth-first search.

Class Diagram:

How to use it:

Pros and cons:

  1. The abstract Menu component class acts as an interface for both leaf node and composite node, thus breaking single responsibility principle.

Before closing out discussion on the collection of objects, touch upon Bounded generics.

Force not to add improper types into your collectibles in the first place. Archiver case.

Below three patterns change the behavior at runtime using composition.

The State Pattern:

Situation:

Encapsulate state-based behavior and delegate behavior to the current state.

Pros and cons:

  1. Lot of classes, one for each state.

The Strategy Pattern:

Situation:

Encapsulate interchangeable behaviors and use delegation to decide which behavior to use.

Configures context classes with a behavior.

Template Method Pattern:

Situation:

Subclasses decide how to implement steps in an algorithm.

Factory pattern:

  1. Tying your class to a concrete implementation (new) is very fragile and less flexible.

Situation: you have different closely related concrete classes and you choose to instantiate one of these based some conditional logic.

Lame solution:

Put if, else blocks and use the new operator to instantiate an appropriate object in each block.

Maintenance problems:

If there is a new object (new duck type), that has to be added to this conditional logic and you have to figure out and add it in all places wherever it is applicable. This is error-prone.

Other solution:

Code to an interface.

Here, we have to figure out which implementation to instantiate for what type. This requires a piece of conditional logic code. This has to change if new implementations are added or any of the existing implementations are to be removed. So, this is not closed for modification.

Factory method lets subclasses decide which class to instantiate.

Observer Pattern:

Situation:

  1. When a group of objects need to be notified of some state changes.

Miscellaneous:

  1. Code to an interface, not to an implementation.
  2. Use bounded generics instead of Object collectibles for better validation and type casting issues.
  3. Usually, an anti-pattern to modify objects coming in as arguments. Use final modifiers.

You may or may not use any of these patterns in your daily life, but understanding these and going through pros and cons of them will significantly impact your thought process and help you make better decisions.

 

 

Automatic Speech Recognition

How do humans hear the speech (5:25)- Introduction on how evolution did it:

An organ in our ear called cochlea has a specialized contribution to our auditory system. It is designed to be responsive to frequency and move variably specific areas along the basilar membrane in response to different frequencies of sound. Based on the area in which basilar membrane moved, different nerve impulses are triggered and informed the brain. A step in the process of extracting Mel frequency cepstral coefficients(popular features for ASR), called periodogram extraction, does a very similar thing.

Mel frequency cepstral coefficients:

Steps to prepare MFCCs:

  1. Split the audio signal into small frames of 20-40 ms, the standard is 25 ms.
  2. Calculate periodogram estimate(power spectrum) for each frame.
  3. Take clumps of periodogram bins and sum the spectrum inside to get the energy levels around different frequencies. We use Mel filterbank to do this. The Mel scale tells us exactly how to space our filterbanks.
  4. Take logarithm of filterbank energies. Humans don’t hear in linear scale as well.
  5. Compute the DCT of log filter bank energies. We do this to decorrelate filterbank energies which are quite correlated. We compress and pick only 12 or 13 coefficients.

Python libraries to extract MFCCs:

  1. scikits.talkbox
  2. librosa
  3. python_speech_features

Learning algorithms for speech recognition:

  1. Using state of the art LSTM recurrent neural networks

 

 


Detailed LSTM tutorial

 

 

 

 

 

Naive Bayes

Bayes theorem helps us to incorporate new evidences/information into our model.

Code from sklearn

from sklearn.naive_bayes import GaussianNB

clf=GaussianNB()

clf.fit(features_train,labels_train)

Bayesian Learning:

Bayesian learning.PNG


Naive bayes

 

Linear in the number of variables.

Naive Bayes assumes conditional independence across attributes and doesn’t capture inter-relationship among attributes.

Gaussian naive Bayes assumes continues values associated with each class are distributed in Gaussian fashion.

Even if the probability of one of the attributes given label becomes zero, the whole thing ends up being zero.


Maximum Likelihood :

Machine learning

Pandas and numpy:

numpy.mean(df[ (df.gold>0) ][“bronze”])

olympic_medal_counts = {‘country_name’:countries,
‘gold’: Series(gold),
‘silver’: Series(silver),
‘bronze’: Series(bronze)}
df = DataFrame(olympic_medal_counts)

del df[‘country_name’]
# YOUR CODE HERE
avg_medal_count=df.apply(lambda x:numpy.mean(x))

b=numpy.array([4,2,1])

a=numpy.column_stack((numpy.array(gold),numpy.array(silver),numpy.array(bronze)))

points=numpy.dot(a,b)

olympic_points_df=DataFrame({‘country_name’:countries,’points’:points})

df[‘points’] = df[[‘gold’,’silver’,’bronze’]].dot([4, 2, 1]) olympic_points_df = df[[‘country_name’,’points’]]


Preprocessing:

For highly-skewed feature distributions such as 'capital-gain' and 'capital-loss', it is common practice to apply a logarithmic transformation on the data so that the very large and very small values do not negatively affect the performance of a learning algorithm. Using a logarithmic transformation significantly reduces the range of values caused by outliers. Care must be taken when applying this transformation however: The logarithm of 0 is undefined, so we must translate the values by a small amount above 0 to apply the the logarithm successfully.

Taking the log of values has the effect of spreading small values and bringing closer to large values.

Scaling:

In addition to performing transformations on features that are highly skewed, it is often good practice to perform some type of scaling on numerical features. Applying a scaling to the data does not change the shape of each feature’s distribution (such as 'capital-gain' or 'capital-loss' above); however, normalization ensures that each feature is treated equally when applying supervised learners. Note that once scaling is applied, observing the data in its raw form will no longer have the same original meaning, as exampled below.

We will use sklearn.preprocessing.MinMaxScaler for this.

If data is not normally distributed, especially if the mean and median vary significantly (indicating a large skew), it is most often appropriate to apply a non-linear scaling — particularly for financial data. One way to achieve this scaling is by using a Box-Cox test, which calculates the best power transformation of the data that reduces skewness. A simpler approach which can work in most cases would be applying the natural logarithm.

Identifying Outliers:

Tukey’s method


 

 

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25)

R2 score:

r2 score.PNG

If {\bar {y}} is the mean of the observed data:

{\bar {y}}={\frac {1}{n}}\sum _{i=1}^{n}y_{i}

then the variability of the data set can be measured using three sums of squares formulas:

SS_{\text{tot}}=\sum _{i}(y_{i}-{\bar {y}})^{2},
SS_{\text{reg}}=\sum _{i}(f_{i}-{\bar {y}})^{2},
{\displaystyle SS_{\text{res}}=\sum _{i}(y_{i}-f_{i})^{2}=\sum _{i}e_{i}^{2}\,}

The most general definition of the coefficient of determination is

R^{2}\equiv 1-{SS_{\rm {res}} \over SS_{\rm {tot}}}.\,

 

Accuracy = true positive + true negatives/total

from sklearn.metrics import accuracy_score

accuracy_score(y_true,y_pred)

Accuracy is not a right metric when data is skewed.


 

Precision:

precision.PNG

Recall:

Recall.PNG

 

f beta.PNG


ROC CURVE:


Errors:

Underfitting: Error due to bias, Oversimplified model, performs badly on both training and testing data.

Overfitting: Error due to variance. Over complicated model. model is too specific, performs badly on testing data.

Model complexity graph:

Model complexity graph.PNG

Training set: for training model.

Cross validation set: for choosing right parameters like degree of the polynomial. Useful to check whether the trained model is overfitting. If trained model performs poorly on this cross validation set, then the model is overfitted.

Testing set: For final testing.

K-FOLD CROSS VALIDATION:

Divide all your data into k buckets and iteratively create models by choosing one bucket as testing set and remaining for training.

Use average of these models for final model.

K-FOLD.PNG

 

If you increase training points on different models:

 

Grid Search CV:

GRID SEARCH CV.PNG


Plot learning curves to identify when to stop collecting data.


Supervised learning:

If there is an order in output data, then go for continuous model. Ex: income, age.

If there is no order, go for a discrete model. Ex: phone numbers, persons


Algorithms to minimize sum of squared errors:

  1. Ordinary least squares: sklearn LinearRegression.
  2. Gradient descent.

There can be multiple lines that minimize |error|, but only one that minimizes error^2.


Instance based learning:

Properties:

  1. Remembers.
  2. Fast and doesn’t learn.
  3. simple.
  4. No generalization.
  5. Sensitive to noise.

 

  1. Look up:

In k-nn all features matter equally because when we calculate distance, all features are treated equally.

 

Locally weighted regression (evolved from k-nearest neighbors):


Naive bayes:

Powerful tools for creating classifiers for incoming labeled data.


Expectation maximization:

expectation maximization.PNG

This is very similar to k-means clustering.

EM is for soft clustering when there is any ambiguity regarding which data point to move to which cluster.


Which supervised classifiers are suitable for numerical as well as categorical data?

The data you have is called ‘mixed data’ because it has both numerical and categorical values. And since you have class labels; therefore, it is a classification problem.  One option is to go with decision trees, which you already tried. Other possibilities are naive Bayes where you model numeric attributes by a Gaussian distribution or so. You can also employ a minimum distance or KNN based approach; however, the cost function must be able to handle data for both types together. If these approaches don’t work then try ensemble techniques. Try bagging with decision trees or else Random Forest that combines bagging and random subspace. With mixed data, choices are limited and you need to be cautious and creative with your choices.


Feature scaling:

To give equal importance to all the different features, we can normalize them to the range of 0 to 1 before applying learning algorithm.

x-x_min/(x_max-x_min)

from sklearn.preprocessing import MinMaxScaler

scaler=MinMaxScaler()

rescaled_weights=scaler.fit_transform(weights)

Feature rescaling would be useful in k-means clustering and rbf svm where we calculate distances but not much in decision trees and linear regression.


Feature selection:

why?

  1. Knowledge discovery, interpretability, and insight. To identify which features actually matter among all of them.
  2. Curse of dimensionality – The amount of data that you need to train grows exponential to the number of features that you have.

NP-HARD


Feature selection:

Filtering(fast) and Wrapping(slow):

knn suffers from curse of dimensionality because it doesn’t know which features are important. So, we can use decision trees as filtering mechanism to determine important features and then pass them on to knn for learning.

Wrapper methods evaluate subsets of variables which allows, unlike filter approaches, to detect the possible interactions between variables.


Relevance:

  1.  A feature is said to be strongly relevant if the Bayes optimal classifier’s performance is strongly affected by the absence of this feature.
  2. A feature is weakly relevant if there exists some other feature which can suffice the purpose of this feature.
  3. Depends on how much information a feature provides.

Usefulness:

  1. Depends on error/model/learner.

Composite feature:

composite feature.PNG


When to use PCA?

  1. When some latent features are driving the patterns in the data.
  2. Dimensionality reduction, reduce noise, better visualization.

Feature transformation:

Independent Component analysis: cocktail party problem.

PCA vs ICA.PNG

Other feature transformations:

  1. Random component analysis – Fast and it usually works.
  2. Linear discriminant analysis –

Lesser the cross entropy, better is the model.

cross entropy is the negative logarithm of probabilities of actual events occurring from the perspective of the model we are trying to evaluate.


 

Difference between RMSE and RMSLE:

RMSLE measures the ratio between actual and predicted.

log(pi+1)log(ai+1)log(pi+1)−log(ai+1)

can be written as log((pi+1)/(ai+1))log((pi+1)/(ai+1))

It can be used when you don’t want to penalize huge differences when both the values are huge numbers.

Also, this can be used when you want to penalize underestimates more than overestimates.

Lets have a look at the below example

Case a) : Pi = 600, Ai = 1000

RMSE = 400, RMSLE = 0.5108

Case b) : Pi = 1400, Ai = 1000

RMSE = 400, RMSLE = 0.3365

As it is evident, the differences are same between actual and predicted in both the cases. RMSE treated them equally however RMSLE penalized the under estimate more than over estimate. Hope this helps.

Design patterns

 

Design that is more automated and require less maintenance is the standard.

Getters and setters:

Setters can be used for validation and constraining the value to be set to a particular range.

Getters can be used for returning default value, if the variable is not set yet or for lazy instantiation.


Can’t make objects out of abstract class. Abstract class can have some non abstract members.

Interface have only abstract methods.


 

Image result for design patterns java


Creational:

  1. Singleton:
    1. Can only have one instance of that particular class.
    2. President of a country, System in java.
    3. Private constructor, singleton using enum.
    4. @Singleton annotation.
    5. Difficult to unit test – why?
  2. Factory:
    1. Having a logic to return a particular subclass object, when asked for a class object.
  3. Abstract Factory:
  4. Builder:
    1. Separates object construction from its representation.
    2. interfaces.
  5. Prototype:
    1. Chess game initial setup.
    2. Copying/cloning the initial setup rather than creating the initial setup everytime you need it. Reduce redundant work.
    3. Copy a fully initialized instance.
    4. Link to code.

How to create objects?

Structural:

Inheritance? Interface? etc.

How are different classes related?

How are objects composed?

  1. Adapter:
    1.  Match interfaces of different classes. helps to communicate.
  2. Composite:
  3. Proxy:
    1. An object representing another object, like credit card as a proxy of bank account.
    2. Remote object and Home object(proxy).
  4. Flyweight:
    1. Reuse same objects by resetting values of the objects appropriately instead of creating new objects every time.
  5. Facade:
    1. Event managers, process, execute, group many steps into a single step.
  6. Bridge:
  7. Decorator:
    1. Add responsibilities to objects dynamically.
    2. Ex: adding different Toppings for different pizzas, adding discounts to different orders.

Behavioral:

Interactions between different objects.

  1. Template method:
  2. Mediator:
    1. instead of applications talking to each other, we use an enterprise service bus.
  3. Chain of responsibility:
    1. Passing a request through different objects.
  4. Observer:
    1. A way of notifying a change to a number of classes.
    2. This pattern is implemented in java.
    3. Subject extends Observable.
    4. Who wants to listen implements Observer and registers with the subject.
  5. Strategy:
    1. change the implementation/strategy of an interface at a later point in time.
    2. Pass whatever implementation needs to be used as an argument.
  6. Command:
    1. Encapsulate a command request as an object.
    2. java.lang.runnable threads are implemented like this.
  7. State:
  8. Visitor:
    1. Adding new operations to a particular class without inheritance and wi
  9. Iterator:
    1. Sequentially access the elements of a collection.
  10. Interpreter:
  11. Memento:
    1. Saving states of something as objects to restore them in future point of time if necessary.
    2. Undo/Redo operations.

Strategy pattern:

What:

 

Strategy design pattern.PNG

When:

Strategy pattern - when.PNG


Observer pattern:

when:

Observer pattern - when

What:

Observer pattern

Factory pattern :

Factory pattern - whenFactory pattern

Abstract Factory pattern:

Singleton pattern:

Singleton pattern.PNG

 Builder pattern:

Builder pattern.PNG

Prototype pattern:


Try to put state and behaviors in different classes.