CS 5043: HW5: Probabilistic Neural Networks

DRAFT

• Deadline: Thursday, April 10th @11:59pm.

• Hand-in procedure: submit a zip file to Gradescope

• This work is to be done on your own. However, you may share solution-specific code snippets in the open on Slack (only!), but not full solutions. Downloading solution-specific materials (text and code) is not allowed (from web pages or from LLMs).

The Problem

The measured variables are described in the Mesonet Daily Summary Data document. For this assignment we will be predicting the rainfall for the day (RAIN) given the other measured variables at the station. These variables are:

• TMAX
• TMIN
• TAVG
• DMAX
• DMIN
• DAVG
• VDEF
• SMAX
• SMIN
• SAVG
• BMAX
• BMIN
• BAVG
• HMAX
• HMIN
• HAVG
• PMAX
• PMIN
• PAVG
• MSLP
• AMAX
• ATOT
• WSMX
• WSMN
• WSPD
• WDEV
• WMAX
• 9AVG
• 2MAX
• 2MIN
• 2AVG
• 2DEV
• HDEG
• CDEG
• HTMX
• WCMN

Supporting Code

• Loading Datasets

      get_mesonet_folds(dataset_fname:str,
                        ntrain_folds: int = 6, 
                        nvalid_folds: int = 1, 
                        ntest_folds: int = 1,
                        rotation: int = 0)
  

  • Returns numpy arrays: ins_training, outs_training, ins_validation, outs_validation, ins_testing, outs_testing

  • Each fold contains different Mesonet stations

• Sinh-Arcsinh Distribution Implementation

  The SinhArcsinh class provides three key class methods:

  • num_params() returns the number of parameters required for this distribution. Each parameter will require one Tensor (one each for mean, standard deviation, skewness, and tailweight).

  • create_layer() returns a proper Keras 3 Layer. This layer is callable with a sequence of 4 Keras Tensors. The implementation assumes that standard deviation and tailweight are only positive. When passed TF Tensor data, the layer returns Tensorflow Probability Distributions (not TF Tensors)

  • mdn_loss(y, dist) Can be used as a loss function for the purposes of compiling your outer model. It returns the negative log likelihood for each true value (y) given the parameterized distribution (dist).

• Probabilistic Neural Networks Demo: pnn-solution.ipynb
  • Synthetic data

  • Normal distribution

Deep Learning Experiment

Model specifics:

• The Sinh-Arcsinh distribution has four input parameters: mean, standard deviation, skewness and tailweight. Each of these parameters is actually a vector -- one element for each input example (specifically, these parameter values are conditioned on the mesonet station data).

• The standard deviation and tailweight must be strictly positive. Your inner model must enforce this (the standard is to use the softplus non-linearity). The other two parameters are unbounded.

• Use negative log likelihood as the loss function.

• Make sure to allocate an appropriate set of hidden layers (and hidden layer sizes) for your inner model.

Performance Reporting

1. Figure 0: Inner network architecture from plot_model().

2. Figures 1a,b: Training and validation set negative likelihood as a function of epoch for each rotation (each figure has six curves).

3. Figure 2: Several time-series examples from a test data set. Show observed precipitation, and curves for distribution mean, and the 10, 25, 75, and 90th distribution percentiles. Make sure to pick interesting time periods.

4. Figures 3a,b,c,d: Combining the test data for all six rotations, show a scatter plot of predicted mean, standard deviation, skewness, and tailweight as a function of observed precipitation.

5. Figure 4: For each rotation, compute the root mean squared difference between observed precipitation, and both the median and mean predicted precipitation. Show these RMSDs using a bar plot with twelve bars. Organize logically.

6. Reflection:
   1. Discuss in detail how consistent your model performance is across the different rotations.

   2. Given the time-series plots, describe and explain the shape of the pdf and how it changes with time.

   3. Discuss how skewness is used by the model. Is there a consistent variation in this distribution parameter?

   4. Discuss how tailweight is used by the model. Is there a consistent variation in this distribution parameter?

   5. Is Sinh-Arcsinh an appropriate distribution for modeling this particular phenomena? Why or why not? (answer in detail)

Hints

• You should be working from the structure of the PNN demo code that we released this week (inner/outer model design, with the outer model returning a probability distribution).

• model_outer.predict(...) will return a sequence of samples from the learned distribution (one sample per example in the input, conditioned on the corresponding input).

• model_outer(...) will return a sequence of distributions (one distribution per example in the input, also conditioned on the inputs)

• The range of the input variables varies dramatically depending on the variable itself. Make sure to add a batch normalization step between your inputs and your first hidden layer. You might also see some benefit to batch normalization at other stages of your network, or by using kernel initializations that limit the magnitude of your initial parameters (but don't set your weights to zeros)

• Be patient with your training. You can gain a lot from this

• See the SinhArcsinh distribution documentation for things you can do with parameterized distributions (useful for creating some of the figures)

• Remember that Tensorflow Probability is very sensitive to the specific combination of package versions that are available in the dnn environment

• You won't need to use a GPU for this assignment

What to Hand In

• All of your python code (.py) and any notebook files (.ipynb)
• Figures 0-4
• Reflection

Do not turn in pickle files.

Grading

• 10 pts: Clean, general code for model building (including in-code documentation)
• 10 pts: Figure 0
• 10 pts: Figure 1
• 10 pts: Figure 2
• 10 pts: Figure 3
• 10 pts: Figure 4
• 15 pts: Reasonable test set performance for all rotations.
• 25 pts: Reflection

andrewhfagg -- gmail.com

Last modified: Wed Apr 2 00:10:26 2025