class_docstr: Linear Kernel.
  
  Is based on the dot product covariance function and can be obtained
  from linear regression. This kernel, when parameterizing a
  Gaussian Process, results in random linear functions.
  The Linear kernel is based on the Polynomial kernel without the
  exponent.
  
  ```none
  k(x, y) = bias_amplitude**2 + slope_amplitude**2 *
            ((x - shift) dot (y - shift))
  ```
class_docstr_tok: ["Linear","Kernel",".","Is","based","on","the","dot","product","covariance","function","and","can","be","obtained","from","linear","regression",".","This","kernel",",","when","parameterizing","a","Gaussian","Process",",","results","in","random","linear","functions",".","The","Linear","kernel","is","based","on","the","Polynomial","kernel","without","the","exponent",".","``","`","none","k","(","x",",","y",")","=","bias_amplitude","*","*","2","+","slope_amplitude","*","*","2","*","(","(","x","-","shift",")","dot","(","y","-","shift",")",")","``","`"]
code: def _parameter_properties(cls, dtype):
      from tensorflow_probability.python.bijectors import (
          softplus,
      )  # pylint:disable=g-import-not-at-top
  
      return dict(
          bias_amplitude=parameter_properties.ParameterProperties(
              default_constraining_bijector_fn=(
                  lambda: softplus.Softplus(low=dtype_util.eps(dtype))
              )
          ),
          slope_amplitude=parameter_properties.ParameterProperties(
              default_constraining_bijector_fn=(
                  lambda: softplus.Softplus(low=dtype_util.eps(dtype))
              )
          ),
          shift=parameter_properties.ParameterProperties(),
      )
  
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.math.psd_kernels import positive_semidefinite_kernel
  from tensorflow_probability.python.math.psd_kernels.internal import util
label_desc: Use image node_id 2 for calling the Linear obj's underlying member method code with example usage: obj._parameter_properties(cls, dtype) and returns: dict