# Tensorflow Lattice – A framework for monotone models with variable data

Any model developed when deployed should perform better for different conditions and different data characteristics. The most widely used flexible machine learning and deep learning models will lack the characteristics needed to capture some important relationships in the data and perform as expected in the testing phase. So this is where the Tensorflow network helps us capture some of the monotonic relationships in the data and helps us get a more generalized pattern regardless of the various trends in the data.

**Contents**

- What is a trellis?
- Introduction to the Tensorflow Networks Library
- The Necessity of Tensorflow Networks Library
- Understanding TensorFlow Network Layers
- Benefits of Tensorflow Network
- Summary

**What is a trellis?**

Lattice in simple terms can be understood as the lookup tables used to calculate various values in mathematics. Similarly, the lattice is an interpolated lookup table that can approximate all input and output relationships in the data with the ability to be entered by multiple lookup tables and multiple key values for various data ranges.

Suppose there is a lookup table with values only for right integer values like 0,1,2 etc.

But we want to determine the value of 0.5 from the lookup table. So, in this case, the search values for 0 and 1 are considered and some corresponding mathematical operations are performed to get the approximate value of 0.5. This is where lattices help us to have interpolated lookup tables for values with different ranges and help us get the right optimal value with the flexibility to adapt to various interrelated key values and can be used to approximate multidimensional characteristics. With these 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 Networks Library**

The Tensorflow Networks Library is a dynamic library capable of capturing the different relationships and trends in data, regardless of the noise in the data. The TensorFlow network library is used when higher model accuracy is expected from the model that is set up for testing. Thus, any typical TensorFlow model built using the TensorFlow lattice library and constraints is expected and guaranteed to perform excellently for similar data types on which it is not trained.

The Tensorflow Networks Library takes advantage of lookup tables and works similarly to lookup tables where multiple input values are entered to capture relationships and ensure monotonic behavior for unseen data. The library also allows us to apply certain constraints to satisfy certain requirements for variable data. Now, let’s dive a little deeper into the Tensorflow network library and try to understand some of the library’s constraints.

The TensorFlow network 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 monotony of the developed model.

**The Necessity of Tensorflow Networks Library**

The main need for the Tensorflow network library is due to the constraints that can be applied on the different dimensions of the data which helps us to get a more reliable and generic model that can be used in various applications. Accuracy is not compromised in Tensorflow network modeling regardless of the unexpected trend in the data and Tensorflow network models are not affected at all by outliers as they will be trained appropriately for unseen events.

Let’s summarize some of the key points that lead to the need for the Tensorflow network library.

- Specification of the monotonicity for each characteristic of the input in order to obtain a more robust and generic model. Thus, the output varies relatively depending on the applied monotonicity constraints.
- Specify the feature shapes according to the data used to be concave or convex. Specifying the shape of the function with the monotonicity constraint helps us speed up processing regardless of the dimensions of the data.
- Specifying the range of values for a certain feature set is easy with Unimodality. This helps some features fall within the range of values decided by some subject matter expertise and these features will have the same set of ranges for variable data.
- The semantic representation and the weighting of certain characteristics of the data can be defined accordingly. This therefore ensures that the model is already trained for certain sensitive parameters and highly correlated features. This helps us eradicate problems associated with multicollinearity and helps to obtain a more generic model.
- Various built-in regularizers are provided by the Tensorflow network library that helps us control certain feature sets accordingly and with respect to linear and non-linear relationships in the data.

**Understanding TensorFlow Network Layers**

The Tensorflow lattice library has some layers to normalize features, considers one-dimensional or multi-dimensional inputs, and normalizes inputs to ensure monotonicity and to enforce some constraints for sensitive behavior for variable data. Some of the standard Tensorflow network layers used are

I)** PWL calibration layer **considers some parameters such as lot size and units and transforms the units to turn each of the units into linear functions to track monotonicity for some applied constraints. For multidimensional 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 commonly used keyword arguments are input keypoints, minimum and maximum output ranges, monotony to ensure, and many others.

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 of categorical calibration layer is mentioned as integer values for each input pair and categorical calibration layer is likely to give higher test accuracy compared to PWL calibration layer because in the PWL calibration layer, we have very few monotonicity parameters declare.

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

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

iii)** Parallel Combination Layer **is used to combine the different calibration layers that will be used during modeling. All the layers that will be used to develop the sequential model will be introduced into the parallel combination layer. The output network or layer will be defined immediately after the parallel combining layer.

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

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

iv) **Network layer **from the Tensorflow network 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 different dimensions of the data. The network layer is responsible for functioning as an interpolated lookup table according to the network size mentioned in that respective layer. In the network layer, the network size is mentioned as an integer, and the monotonicity constraints for each of the characteristics can be mentioned as none, increasing, 0, 1. With these monotonicity constraints, some parameters can certain constraints may be imposed and certain parameters may be left as they are. The application of the constraints with respect to the dimension of the data is entirely subjective and conforms to the requirement with respect to the change of the data and the parameters.

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

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

depending on the dimension of the input, monotonicities and many others.

Here are some of the layers offered by the Tensorflow network for building models using the library. Later, the model can be compiled against the split data and suitably compiled for various parameters. The main purpose of using Tensorflow network library is to get a generic model for variable data and uncertain data changes. Thus, the TensorFlow network model can be further leveraged to test by changing the data or validate its performance for unseen or drastic changes in the data.

**Benefits of Tensorflow Network**

Some of the advantages of the Tensorflow network model are listed below.

- A model trained by lattice trained for particular data can be used to train a similar type of data with certain constraints applied.
- Since the constraint set is applied in the Lattice layer, the models obtained from the Tensorflow lattice library are more generic.
- Predefined estimators are pre-trained to quickly learn the required characteristics of the data, regardless of the dimensions of the data.
- Modeling the TensorFlow network is simple and the model parameters are easily interpretable.
- Helps us get an accurate and flexible model and is very flexible with various regularization techniques.

**Summary**

The main goal of any model development is to obtain a reliable and generic model. But in the current situation of data variation with an increasing volume of data, the genericity of data cannot be expected. This is where the Tensorflow network library helps us get a more reliable and generic model. The main goal of network modeling is to achieve high accuracies when tested for similar types of data under different conditions. TensorFlow network models with subject matter expertise apply certain constraints on certain characteristics of the data and depending on the constraints applied, the model performs as expected in different test scenarios.

**References**