denis-bz

NO2 in Munich 2016: high traffic => high NO2

This plot shows NO2 levels over the day in Munich in June and December 2016. München-Landshuter-Allee on the left has about the highest NO2 levels in all Germany, and a lot of traffic — 120,000 to 150,000 cars and light trucks per day.
Surprise: high traffic => high NO2.

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NO2 in Stuttgart, Germany, 2014 - 2016

This plot is from SZ-Tages-Werte-2000-2016.xls from https://www.Stadtklima-Stuttgart.de/index.php?luft_messdaten_download:

The data is "background", not official, from a single measurement station:

Hintergrundmessstation für die Stuttgarter Innenstadt

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EPA air quality: NO2 and ozone in 3 US cities in 2016

The Environmental Protection Agency collects data on NO2, ozone, wind etc. in hundreds of US cities, and puts it in files like daily_TEMP_2015.csv on the web site http://aqsdr1.epa.gov/aqsweb/aqstmp/airdata .

Plots

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color_hilo: color high-water or low-water numbers in a given column

See color_hilo.py below for a description of what this does.

To install on a Unix-like system,

1. click on "Download ZIP" in the top right-hand corner; ls ~/*/*.zip to see where it is, e.g. ~/Downloads/verylongname.zip
2. cd to a directory in your $PYTHONPATH
3. unzip ~/Downloads/verylongname.zip

denis-bz

Gradient descent with 2-point line fit where gradients cross 0

The Gradient_descent method iterates

xnew = xold - rate(t) * grad(xold)

GD is a workhorse in machine learning, because it's so simple, uses gradients only (not function values), and can do very big x.

rate(t) is a step-size or "learning rate" (aka η, Greek eta).

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#!/usr/bin/env python2
""" How many of the longest pieces of a randomly-broken stick add up to half its length ? """
# http://demonstrations.wolfram.com/BrokenStickRule

from __future__ import division
import sys
import numpy as np

__version__ = "2014-10-26 oct  denis-bz-py t-online de"
np.set_printoptions( 1, threshold=100, edgeitems=5, suppress=True )

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#!/usr/bin/env python2
""" min_x av |exp - x| at 0.7  -- W Least_absolute_deviations, L1
    min_x rms( exp - x ) at 1  -- least squares, L2
    are both very flat
    which might explain why L1 minimization with IRLS doesn't work very well.
"""
    # goo "L1 minimization" irls
    # different L1 min problems: sparsity, outliers

from __future__ import division

denis-bz

Adaptive soft threshold and smooth abs: scale by average |X|

The soft threshold and smooth absolute value functions

are widely used in optimization and signal processing. (Soft thresholding squeezes small values to 0; if "noise" is small and "signal" large, this improves the signal-to-noise ratio. Smooth abs, also called

denis-bz

Qmin: minimize a noisy function by fitting quadratics.

Purpose: short, clear code for

• fitting quadratics to data, aka quadratic regression
• iterating quad fits to a local minimum of a noisy function.

This code is for students of programming and optimization to read and try out, not for professionals.

denis-bz

How noisy is test error in classification ?

Algorithms for classification, in particular binary classification, have two different objectives:

• a smooth, fast, approximate Loss function used in most optimizers
• real loss measured on a test set: expensive to calculate, so usually done only at the end.