Machine Learning Interview Cheatsheets

 Cheat  Sheet  –Bias-Variance  Tradeoff

What  is  Bias? • Error  between  average  model  prediction  and  ground  truth • The  bias  of  the  estimated  function  tells  us  the  capacity  of  the  underlying  model  to predict  the  values What  is  Variance? • Average  variability  in  the  model  prediction  for  the  given  dataset • The  variance  of  the  estimated  function  tells  you  how  much  the  function  can  adjust to  the  change  in  the  dataset High  Bias High  Variance Overly-simplified  Model Under-fitting High  error  on  both  test  and  train  data Overly-complex  Model Over-fitting Low  error  on  train  data  and  high  on  test Starts  modelling  the  noise  in  the  input Bias  variance  Trade-off Minimum  Error • Increasing  bias  reduces  variance  and  vice-versa • Error  =  bias2 +  variance  +irreducible  error • The  best  model  is  where  the  error  is  reduced. • Compromise  between  bias  and  variance

What  is  PCA? • Based  on  the  dataset  find  a  new  set  of  orthogonal  feature  vectors  in  such  a  way  that  the data  spread  is  maximum  in  the  direction  of  the  feature  vector  (or  dimension) • Rates  the  feature  vector  in  the  decreasing  order  of  data  spread  (or  variance) • The datapoints  have  maximum  variance  in  the  first  feature  vector,  and  minimum  variance in  the  last  feature  vector • The variance  of  the  datapoints  in  the  direction  of  feature  vector  can  be  termed  as  a measure  of  information  in  that  direction. Steps 1. Standardize  the  datapoints 2. 3. 4. Find  the  covariance  matrix  from  the  given  datapoints Carry  out  eigen-value  decomposition  of  the  covariance  matrix Sort  the  eigenvalues  and  eigenvectors Dimensionality  Reduction  with  PCA • Keep  the  first  m  out  of  n  feature  vectors  rated  by  PCA.  These  m  vectors  will  be  the  best  m vectors  preserving  the  maximum  information  that  could  have  been  preserved  with  m vectors  on  the  given  dataset Steps: 1. Carry  out  steps  1-4  from  above 2. 3. 4. Keep  first  m  feature  vectors  from  the  sorted  eigenvector  matrix Transform  the  data  for  the  new  basis  (feature  vectors) The  importance  of  the  feature  vector  is  proportional  to  the  magnitude  of  the  eigen  value

What  is  Bayes’ Theorem? • Describes the probability of an event, based on prior knowledge of conditions that might be related to the event. • How the probability of an event changes when we have knowledge of another event P(A) P(A B) Example • Probability  of  fire  P(F)  =  1% Usually  a  better estimate  than  P(A) • Probability  of  smoke  P(S)  =  10% • Prob  of  smoke  given  there  is  a  fire  P(S  F)  =  90% • What  is  the  probability  that  there  is  a  fire  given we  see  a  smoke  P(F  S)? P(A  B) Posterior Probability Likelihood Bayes’ Theorem P(A) P(B  A) Prior Probability Evidence P(B) Maximum  Aposteriori Probability  (MAP)  Estimation The MAP estimate of the random variable y, given that we have observed iid (x1, x2, x3, … ), is given by. We try to accommodate our prior knowledge when estimating. ˆ MAP y  that  maximizes  the  product  of prior and  likelihood Maximum  Likelihood  Estimation  (MLE) The MAP estimate of the random variable y, given that we have observed iid (x1, x2, x3, … ), is given by. We assume we don’t have any prior knowledge of the quantity being estimated. ˆ MLE y  that  maximizes  only  the likelihood MLE  is  a  special  case  of  MAP  where  our  prior  is  uniform  (all  values  are  equally  likely) Naïve  Bayes’ Classifier  (Instantiation  of  MAP  as  classifier) Suppose  we  have  two  classes,  y=y1 and  y=y2.  Say  we  have  more  than  one  evidence/features  (x1, x2,  x3,  … ),  using  Bayes’ theorem

What is Regression Analysis? Fitting a function f(.) to datapoints yi=f(xi) under some error function. Based on the estimated function and error, we have the following types of regression 1. Linear Regression: Fits a line minimizing the sum of mean-squared error for each datapoint. 2. Polynomial Regression: Fits a polynomial of order k (k+1 unknowns) minimizing the sum of mean-squared error for each datapoint. 3. Bayesian Regression: For each datapoint, fits a gaussian distribution by minimizing the mean-squared error. As the number of data points xi increases, it converges to point estimates i.e. 4. Ridge Regression: Can fit either a line, or polynomial minimizing the sum of mean-squared error for each datapoint and the weighted L2 norm of the function parameters beta. 5. LASSO Regression: Can fit either a line, or polynomial minimizing the the sum of mean-squared error for each datapoint and the weighted L1 norm of the function parameters beta. 6. Logistic Regression (NOT regression, but classification): Can fit either a line, or polynomial with sigmoid activation minimizing the sum of mean-squared error for each datapoint. The labels y are binary class labels.

Cheat  Sheet  –Regularization  in  ML What  is  Regularization  in  ML? • Regularization is an approach to address over-fitting in ML. • Overfitted model fails to generalize estimations on test data • When the underlying model to be learned is low bias/high variance, or when we have small amount of data, the estimated model is prone to over-fitting. • Regularization reduces the variance of the model Types of Regularization: 1.Modify the loss function: Figure  1.  Overfitting • L2 Regularization: Prevents the weights from getting too large (defined by L2 norm). Larger the weights, more complex the model is, more chances of overfitting. • L1 Regularization: Prevents the weights from getting too large (defined by L1 norm). Larger the weights, more complex the model is, more chances of overfitting. L1 regularization introduces sparsity in the weights. It forces more weights to be zero, than reducing the the average magnitude of all weights • Entropy: Used for the models that output probability. Forces the probability distribution towards uniform distribution. 2.Modify data sampling: • Data augmentation: Create more data from available data by randomly cropping, dilating, rotating, adding small amount of noise etc. • K-fold Cross-validation: Divide the data into k groups. Train on (k-1) groups and test on 1 group. Try all k possible combinations. 3.Change training approach: • Injecting noise: Add random noise to the weights when they are being learned. It pushes the model to be relatively insensitive to small variations in the weights, hence regularization • Dropout: Generally used for neural networks. Connections between consecutive layers are randomly dropped based on a dropout-ratio and the remaining network is trained in the current iteration. In the next iteration, another set of random connections are dropped.

AlexNet –2012 Why: AlexNet was born out of the need to improve the results of the ImageNet challenge. What: The network consists of 5 Convolutional (CONV) layers and 3 Fully Connected (FC) layers. The activation used is the Rectified Linear Unit (ReLU). How: Data augmentation is carried out to reduce over-fitting, Uses Local response localization. VGGNet –2014 Why: VGGNet was born out of the need to reduce the # of parameters in the CONV layers and improve on training time What: There are multiple variants of VGGNet (VGG16, VGG19, etc.) How: The important point to note here is that all the conv kernels are of size 3x3 and maxpool kernels are of size 2x2 with a stride of two. ResNet –2015 Why: Neural Networks are notorious for not being able to find a simpler mapping when it exists. ResNet solves that. What: There are multiple versions of ResNetXX architectures where ‘XX’ denotes the number of layers. The most used ones are ResNet50 and ResNet101. Since the vanishing gradient problem was taken care of (more about it in the How part), CNN started to get deeper and deeper How: ResNet architecture makes use of shortcut connections do solve the vanishing gradient problem. The basic building block of ResNet is a Residual block that is repeated throughout the network.

Cheat Sheet –Convolutional Neural NetworkConvolutionalNeuralNetwork:ThedatagetsintotheCNNthroughtheinputlayerandpassesthroughvarioushiddenlayersbeforegettingtotheoutputlayer.Theoutputofthenetworkiscomparedtotheactuallabelsintermsoflossorerror.Thepartialderivativesofthislossw.r.tthetrainableweightsarecalculated,andtheweightsareupdatedthroughoneofthevariousmethodsusingbackpropagation.CNNTemplate:Mostofthecommonlyusedhiddenlayers(notall)followapattern1.Layerfunction:Basictransformingfunctionsuchasconvolutionalorfullyconnectedlayer.a.FullyConnected:Linearfunctionsbetweentheinputandtheoutput.-2.0-1.00.01.02.00.00.51.01.52.02.53.03.54.0MSELossmse=(x°ˆx)2mse=(x°ˆx)2-2.0-1.00.01.02.00.00.250.50.751.01.251.51.752.0MAELossmae=|x°ˆx|mae=|x°ˆx|-2.0-1.00.01.02.00.00.250.50.751.01.251.51.752.0HuberLossΩ12(x°ˆx)2:|x°ˆx|<∞∞|x°ˆx|°12∞2:elseæ∞=1.9Ω12(x°ˆx)2:|x°ˆx|<∞∞|x°ˆx|°12∞2:elseæ∞=1.9-2.0-1.00.01.02.00.00.51.01.52.02.53.0HingeLossΩmax(0,1°ˆx):x=1max(0,1+ˆx):x=°1æΩmax(0,1°ˆx):x=1max(0,1+ˆx):x=°1æ0.00.20.40.60.81.00.02.04.06.08.0CrossEntropyLoss°ylog(p)°(1°y)log(1°p)°ylog(p)°(1°y)log(1°p)0.00.20.40.60.81.00.00.20.40.60.81.0Input MapKernelOutput MapConvolutional Layera.ConvolutionalLayers:Theselayersareappliedto2D(3D)inputfeaturemaps.Thetrainableweightsarea2D(3D)kernel/filterthatmovesacrosstheinputfeaturemap,generatingdotproductswiththeoverlappingregionoftheinputfeaturemap.b.TransposedConvolutional(DeConvolutional)Layer:Usuallyusedtoincreasethesizeoftheoutputfeaturemap(Upsampling)Theideabehindthetransposedconvolutionallayeristoundo(notexactly)theconvolutionallayer2.Pooling:Non-trainablelayertochangethesizeofthefeaturemapa.Max/AveragePooling:Decreasethespatialsizeoftheinputlayerbasedonselectingthemaximum/averagevalueinreceptivefielddefinedbythekernelb.UnPooling:Anon-trainablelayerusedtoincreasethespatialsizeoftheinputlayerbasedonplacingtheinputpixelatacertainindexinthereceptivefieldoftheoutputdefinedbythekernel.3.Normalization:Usuallyusedjustbeforetheactivationfunctionstolimittheunboundedactivationfromincreasingtheoutputlayervaluestoohigha.LocalResponseNormalizationLRN:Anon-trainablelayerthatsquare-normalizesthepixelvaluesinafeaturemapwithinalocalneighborhood.b.BatchNormalization:Atrainableapproachtonormalizingthedatabylearningscaleandshiftvariableduringtraining.3.Activation:Introducenon-linearitysoCNNcanefficientlymapnon-linearcomplexmapping.a.Non-parametric/Staticfunctions:Linear,ReLUb.Parametricfunctions:ELU,tanh,sigmoid,LeakyReLUc.Boundedfunctions:tanh,sigmoid5.Lossfunction:QuantifieshowfarofftheCNNpredictionisfromtheactuallabels.a.RegressionLossFunctions:MAE,MSE,Huberlossb.ClassificationLossFunctions:Crossentropy,Hingeloss

Cheat  Sheet  –Ensemble  Learning  in  ML What is Ensemble Learning? Wisdom of the crowd Combine multiple weak models/learners into one predictive model to reduce bias, variance and/or improve accuracy. Types of Ensemble Learning: N number of weak learners 1.Bagging: Trains N different weak models (usually of same types –homogenous) with N non-overlapping subset of the input dataset in parallel. In the test phase, each model is evaluated. The label with the greatest number of predictions is selected as the prediction. Bagging methods reduces variance of the prediction 2.Boosting: Trains N different weak models (usually of same types –homogenous) with the complete dataset in a sequential order. The datapoints wrongly classified with previous weak model is provided more weights to that they can be classified by the next weak leaner properly. In the test phase, each model is evaluated and based on the test error of each weak model, the prediction is weighted for voting. Boosting methods decreases the bias of the prediction. 3.Stacking: Trains N different weak models (usually of different types –heterogenous) with one of the two subsets of the dataset in parallel. Once the weak learners are trained, they are used to trained a meta learner to combine their predictions and carry out final prediction using the other subset. In test phase, each model predicts its label, these set of labels are fed to the meta learner which generates the final prediction.