# Tensorflow Lattice- A framework for monotonic models with varying data

Tensorflow lattice modelling aims to obtain a more reliable and generic model which perfroms phenomanally when taken up for testing for similar kind of data it is trained upon.
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Any model developed when deployed is expected to perform better for different conditions and varying data characteristics. Mostly used flexible machine learning and deep learning models will not have the characteristics to capture certain important relationships in the data and perform as expected in the testing phase. So this is where the Tensorflow lattice helps us to capture some of the monotonic relationships in the data and helps us in obtaining a more generalized model irrespective of various trends in the data.

1. What is a lattice?
2. Introduction to the Tensorflow lattice library
3. The necessity of the Tensorflow lattice library
4. An overview of  TensorFlow lattice layers
5. Benefits of Tensorflow lattice
6. Summary

## What is a lattice?

Lattice in simple terms can be understood as the lookup tables used to compute various values in mathematics. In a similar way, the lattice is an interpolated look-up table that can approximate any input and output relationships in the data with the ability to be keyed by multiple lookup tables and multiple key values for various ranges of data.

Say suppose there is a lookup table with values only for right integer values like 0,1,2,.. Etc.

#### THE BELAMY

But we want to determine the value of 0.5 from the look-up table. So in this case the lookup value for 0 and 1 are considered and some corresponding mathematical operations are performed to obtain the approximate value for 0.5. This is where lattices help us to have interpolated look-up tables for values with various ranges and help us obtain the right optimal value with the flexibility of adapting for various interrelated key values and can be used to approximate multi-dimensional features. With this multiple input and output relationships in the data and various characteristics of the data can be captured using Lattices.

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## Introduction to the Tensorflow lattice library

The Tensorflow lattice library is a dynamic library with the ability to capture the various relationships and trends of the data irrespective of the noise in the data. The TensorFlow lattice library is used when higher model accuracy is expected from the model which is put up for testing. So any typical TensorFlow model built by using the TensorFlow lattice library and constraints is expected and guaranteed for excellent behavior for similar kinds of data which it is not trained upon.

The Tensorflow lattice library takes the advantage of the lookup tables and operates in a similar manner to the lookup tables where multiple input values are keyed to capture the relationships and ensure monotonic behavior for unseen data.  The library also allows us to enforce certain constraints to satisfy certain requirements for varying data. Now let us dive a little deep into the Tensorflow lattice library and try to understand some of the constraints of the library.

The TensorFlow lattice library can be easily integrated into any of the Keras models for monotonicity. The library uses certain functions and estimators and offers certain layers to ensure the monotonicity of the model developed.

## The necessity of the Tensorflow lattice library

The main necessity of the Tensorflow lattice library is due to the constraints that can be enforced on the various dimensions of the data that help us to obtain a more reliable and generic model that can be used in various applications. Accuracy is not compromised in Tensorflow lattice modeling irrespective of the unexpected trend in data and Tensorflow lattice models are not at all affected by outliers as they will be trained suitably for unseen events.

Let us summarize some of the key points which bring in the necessity of the Tensorflow lattice library.

• Specifying monotonicity for each feature of the input to obtain a more robust and generic model. So the output relatively varies according to the monotonicity constraints enforced.
• Specifying the shapes of function according to the data in use to be concave or convex. Specifying the shape of function with the monotonicity constraint helps us in faster processing irrespective of the dimensions of the data.
• Specifying the range of values for a certain set of features is easy through Unimodality. This helps certain features to lie within the range of values decided by certain subject expertise and these features will have the same set of range for varying data.
• Semantic representation and weightage for certain features of the data can be set accordingly. So this ensures that the model is already trained for certain sensitive parameters and highly correlated features. This helps us to eradicate the problems associated with multicollinearity and helps in obtaining a more generic model.
• Various inbuilt regularizers are provided by the Tensorflow lattice library that helps us to control certain sets of features accordingly and with respect to the linear and nonlinear relationships in data.

## An overview of  TensorFlow lattice layers

The Tensorflow lattice library has certain layers for normalizing features, considers the single or multi-dimensional inputs, and normalizes the inputs to ensure monotonicity and to enforce certain constraints for sensible behavior for varying data. Some of the standard Tensorflow lattice layers being used are

i) PWL Calibration layer considers certain parameters such as batch size and units and transforms the units to transform each of the units to linear functions to follow monotonicity for certain constraints enforced. For multi-dimensional data, each of the input units will be transformed according to the constraints for each of the input dimensions or each of the inputs will be transformed according to a single constraint for each of the inputs.

Syntax: tfl.layers.PWLCalibration(**kwargs)

Some of the keyword arguments generally used are input keypoints, minimum and maximum output ranges, monotonicity to be ensured, and many more.

ii) Categorical Calibration layer is similar to the PWL calibration layer. But the parameters used in the categorical calibration layer are different from the PWL calibration layer. The monotonicity for the categorical calibration layer is mentioned in form of integer values for each pair of inputs and the categorical calibration layer is prone to yield higher testing accuracy when compared to the PWL calibration layer as in the PWL calibration layer we have very few monotonicity parameters to declare.

Syntax:  tfl.layers.CategoricalCalibration(**kwargs)

Some of the standard keyword arguments include the number of buckets, monotonicity as a set of integers, and many more.

iii) Parallel Combination layer is used to combine the various calibration layers that will be used while modeling. All the layers that will be used to develop the Sequential model will be fed into the parallel combination layer. The lattice or the output layer will be defined immediately after the parallel combination layer.

Syntax: tfl.layers.ParallelCombination(**kwargs)

Some of the most used arguments in the Parallel Combination layer are the list of calibration layers, output tensors required, and many more.

iv) Lattice Layer of the Tensorflow lattice library is the most important layer and this layer is used for modeling. The layer is responsible for performing the interpolation with respect to the various dimensions of data. The lattice layer is responsible for operating like an interpolated look-up table according to the lattice size mentioned in this respective layer. In the lattice layer, the lattice size is mentioned in the form of an integer, and monotonicity constraints for each of the features can be mentioned as none, increasing,0, 1. With these constraints of monotonicity, certain parameters can be enforced certain constraints and certain parameters can be left as it is. The constraint enforcement with respect to the dimension of the data is entirely subjective and as per the requirement with respect to the change in data and parameters.

Syntax: tfl.layers.Lattice(**kwargs)

Some of the most used keyword arguments in the lattice layer include the lattice sizes, units

based on the dimension of the input, monotonicities, and many more.

These are some of the layers that Tensorflow lattice offers for model creation using the library. Later the model can be compiled against the split data and suitably compiled for various parameters. The main aim of using the Tensorflow lattice library is to obtain a generic model for varying data and uncertain data changes. So the TensorFlow lattice model can be more emphasized to test by changing the data or validate its performance for unseen or drastic changes in the data.

## Benefits of Tensorflow lattice

Some of the benefits of the Tensorflow lattice model are as listed below.

• A lattice-trained model trained for a particular data can be used for training a similar kind of data with certain constraints being enforced.
• With the set of constraints being enforced in the Lattice layer, the models obtained from the Tensorflow lattice library are more generic.
• The prebuilt estimators are pre-trained to quickly learn the required features of the data irrespective of the dimensions of the data.
• The TensorFlow lattice modeling is easy and the model parameters are easily interpretable.
• Helps us to obtain an accurate and flexible model and is highly flexible with various regularization techniques.

## Summary

The main purpose of any model development is to obtain a reliable and generic model. But in the current situation of variation in data with increasing volume data genericness cannot be expected. This is where the Tensorflow lattice library helps us to obtain a more reliable and generic model. The main purpose of lattice modeling is to obtain high accuracies when tested for similar kinds of data under different conditions. TensorFlow lattice models with subject expertise enforce certain constraints on certain features of the data and according to the constraints enforced the model performs as expected under different testing scenarios.

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Darshan is a Master's degree holder in Data Science and Machine Learning and an everyday learner of the latest trends in Data Science and Machine Learning. He is always interested to learn new things with keen interest and implementing the same and curating rich content for Data Science, Machine Learning,NLP and AI

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