# Parameter transformations

This tutorial builds on the [linear regression
tutorial](01-lin-reg.md#linear-regression). Here, we demonstrate how we
can easily transform a parameter in our model to sample it with NUTS
instead of a Gibbs Kernel.

First, let’s set up our model again. This is the same model as in the
[linear regression tutorial](01-lin-reg.md#linear-regression), so we
will not go into the details here.

``` python
import jax
import jax.numpy as jnp
import liesel.goose as gs
import liesel.model as lsl
import matplotlib.pyplot as plt
import numpy as np

# We use distributions and bijectors from tensorflow probability
import tensorflow_probability.substrates.jax.distributions as tfd
import tensorflow_probability.substrates.jax.bijectors as tfb

rng = np.random.default_rng(42)

# data-generating process
n = 500
true_beta = np.array([1.0, 2.0])
true_sigma = 1.0
x0 = rng.uniform(size=n)
X_mat = np.column_stack([np.ones(n), x0])
eps = rng.normal(scale=true_sigma, size=n)
y_vec = X_mat @ true_beta + eps

# Model
# Part 1: Model for the mean
beta_loc = lsl.Var(0.0, name="beta_loc")
beta_scale = lsl.Var(100.0, name="beta_scale") # scale = sqrt(100^2)
beta_dist = lsl.Dist(tfd.Normal, loc=beta_loc, scale=beta_scale)
beta = lsl.Param(value=np.array([0.0, 0.0]), distribution=beta_dist,name="beta")

X = lsl.Obs(X_mat, name="X")
calc = lsl.Calc(lambda x, beta: jnp.dot(x, beta), x=X, beta=beta)
y_hat = lsl.Var(calc, name="y_hat")

# Part 2: Model for the standard deviation
sigma_a = lsl.Var(0.01, name="a")
sigma_b = lsl.Var(0.01, name="b")
sigma_dist = lsl.Dist(tfd.InverseGamma, concentration=sigma_a, scale=sigma_b)
sigma = lsl.Param(value=10.0, distribution=sigma_dist, name="sigma")

# Observation model
y_dist = lsl.Dist(tfd.Normal, loc=y_hat, scale=sigma)
y = lsl.Var(y_vec, distribution=y_dist, name="y")
```

Now let’s try to sample the full parameter vector
$(\boldsymbol{\beta}', \sigma)'$ with a single NUTS kernel instead of
using a NUTS kernel for $\boldsymbol{\beta}$ and a Gibbs kernel for
$\sigma^2$. Since the standard deviation is a positive-valued parameter,
we need to log-transform it to sample it with a NUTS kernel. The
{class}`.GraphBuilder` class provides the {meth}`.transform_parameter`
method for this purpose.

``` python
gb = lsl.GraphBuilder().add(y)
```

    liesel.model.model - INFO - Converted dtype of Data(name="y_value").value
    liesel.model.model - INFO - Converted dtype of Data(name="beta_value").value
    liesel.model.model - INFO - Converted dtype of Data(name="X_value").value

``` python
gb.transform(sigma, tfb.Exp)
```

    Var(name="sigma_transformed")

    No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)

``` python
model = gb.build_model()
lsl.plot_vars(model)
```

![](01a-transform_files/figure-commonmark/graph-and-transformation-1.png)

The response distribution still requires the standard deviation on the
original scale. The model graph shows that the back-transformation from
the logarithmic to the original scale is performed by a inserting the
`sigma_transformed` and turning the `sigma` node into a weak node. This
weak node deterministically depends on `sigma_transformed`: its value is
the back-transformed standard deviation.

Now we can set up and run an MCMC algorithm with a NUTS kernel for all
parameters.

``` python
builder = gs.EngineBuilder(seed=1339, num_chains=4)

builder.set_model(lsl.GooseModel(model))
builder.set_initial_values(model.state)

builder.add_kernel(gs.NUTSKernel(["beta", "sigma_transformed"]))

builder.set_duration(warmup_duration=1000, posterior_duration=1000)

# by default, goose only stores the parameters specified in the kernels.
# let's also store the standard deviation on the original scale.
builder.positions_included = ["sigma"]

engine = builder.build()
```

    liesel.goose.builder - WARNING - No jitter functions provided. The initial values won't be jittered
    liesel.goose.engine - INFO - Initializing kernels...
    liesel.goose.engine - INFO - Done

``` python
engine.sample_all_epochs()
```

    liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 75 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 4, 4, 3, 3 / 75 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 25 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 2, 2, 1, 2 / 25 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 50 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 1, 1, 2 / 50 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 100 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 6, 3, 2, 2 / 100 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 200 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 2, 2, 2, 1 / 200 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 500 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 2, 1, 2, 3 / 500 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 50 transitions, 25 jitted together
    liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 2, 2, 1 / 50 transitions
    liesel.goose.engine - INFO - Finished epoch
    liesel.goose.engine - INFO - Finished warmup
    liesel.goose.engine - INFO - Starting epoch: POSTERIOR, 1000 transitions, 25 jitted together
    liesel.goose.engine - INFO - Finished epoch

Judging from the trace plots, it seems that all chains have converged.

``` python
results = engine.get_results()
g = gs.plot_trace(results)
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1057: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.
      grouped_data = data.groupby(

![](01a-transform_files/figure-commonmark/traceplots-3.png)

We can also take a look at the summary table, which includes the
original $\sigma$ and the transformed $\log(\sigma)$.

``` python
gs.Summary.from_result(results)
```

<div class="cell-output-display">

<p>
<strong>Parameter summary:</strong>
</p>
<table border="0" class="dataframe">
<thead>
<tr style="text-align: right;">
<th>
</th>
<th>
</th>
<th>
kernel
</th>
<th>
mean
</th>
<th>
sd
</th>
<th>
q_0.05
</th>
<th>
q_0.5
</th>
<th>
q_0.95
</th>
<th>
sample_size
</th>
<th>
ess_bulk
</th>
<th>
ess_tail
</th>
<th>
rhat
</th>
</tr>
<tr>
<th>
parameter
</th>
<th>
index
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
</tr>
</thead>
<tbody>
<tr>
<th rowspan="2" valign="top">
beta
</th>
<th>
(0,)
</th>
<td>
kernel_00
</td>
<td>
0.987
</td>
<td>
0.090
</td>
<td>
0.837
</td>
<td>
0.985
</td>
<td>
1.133
</td>
<td>
4000
</td>
<td>
1172.348
</td>
<td>
1669.813
</td>
<td>
1.005
</td>
</tr>
<tr>
<th>
(1,)
</th>
<td>
kernel_00
</td>
<td>
1.903
</td>
<td>
0.158
</td>
<td>
1.652
</td>
<td>
1.904
</td>
<td>
2.159
</td>
<td>
4000
</td>
<td>
1135.497
</td>
<td>
1573.939
</td>
<td>
1.005
</td>
</tr>
<tr>
<th>
sigma
</th>
<th>
()
</th>
<td>
\-
</td>
<td>
1.022
</td>
<td>
0.033
</td>
<td>
0.969
</td>
<td>
1.021
</td>
<td>
1.077
</td>
<td>
4000
</td>
<td>
2221.160
</td>
<td>
2215.311
</td>
<td>
1.001
</td>
</tr>
<tr>
<th>
sigma_transformed
</th>
<th>
()
</th>
<td>
kernel_00
</td>
<td>
0.021
</td>
<td>
0.032
</td>
<td>
-0.032
</td>
<td>
0.021
</td>
<td>
0.074
</td>
<td>
4000
</td>
<td>
2221.171
</td>
<td>
2215.311
</td>
<td>
1.001
</td>
</tr>
</tbody>
</table>
<p>
<strong>Error summary:</strong>
</p>
<table border="0" class="dataframe">
<thead>
<tr style="text-align: right;">
<th>
</th>
<th>
</th>
<th>
</th>
<th>
</th>
<th>
count
</th>
<th>
relative
</th>
</tr>
<tr>
<th>
kernel
</th>
<th>
error_code
</th>
<th>
error_msg
</th>
<th>
phase
</th>
<th>
</th>
<th>
</th>
</tr>
</thead>
<tbody>
<tr>
<th rowspan="2" valign="top">
kernel_00
</th>
<th rowspan="2" valign="top">
1
</th>
<th rowspan="2" valign="top">
divergent transition
</th>
<th>
warmup
</th>
<td>
60
</td>
<td>
0.015
</td>
</tr>
<tr>
<th>
posterior
</th>
<td>
0
</td>
<td>
0.000
</td>
</tr>
</tbody>
</table>

</div>

The effective sample size is higher for $\sigma$ than for
$\boldsymbol{\beta}$. Finally, let’s check the autocorrelation of the
samples.

``` python
g = gs.plot_cor(results)
```

    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead
      if pd.api.types.is_categorical_dtype(vector):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):
    /opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/seaborn/_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.
      with pd.option_context('mode.use_inf_as_na', True):

![](01a-transform_files/figure-commonmark/correlation-plots-5.png)