# [R] Improve training of predictive neural networks

Bert Gunter bgunter.4567 at gmail.com
Thu Jan 14 00:08:25 CET 2016

```Inline.

-- Bert
Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Wed, Jan 13, 2016 at 2:55 PM, Luigi Marongiu
<marongiu.luigi at gmail.com> wrote:
> Dear all,
> I am trying to train a predictive neural network to guess the
> positivity/negativity of some tests I have done. I am using the
> library pnn and I have empirically identified the best sigma to use in
> the algorithm but the results I got are affected by false positive
> results.
> The actual dataset I am using is formed by 14,000 values, which I have
> subdivided in a training and query subsets. Since the numbers are high
> I can't really use them for the present example, just suffice to say
> that the values less than y = 0.035 are negative in the training
> subset. However in the query subset many values with y < 0.035 and x
> between about 10 and 30 are given as positive.
> Since the only parameter that I can change in pnn is essentially sigma
> and the training subset is properly dividing the positive and negative
> populations, how can I further train the system to reduce the false
> positive rate?

You cannot. You have already allowed the results on the query subset
to feed back to your training procedure, which completely invalidates
the procedure. You get one bite at the apple, no more.  From here on,
you will most likely produce irreproducible nonsense.

As this is all about the proper use of statistical procedures and not
at all about R, per se, I suggest you follow up by posting on a
statistical site like stats.stackexchange.com, not here.

Cheers,
Bert

> In the example I am using here, which is just an approximation of the
> real thing, red and black circles indicates the positive and negative
> values of the training subset, respectively. Squares comes from the
> query subset, red/black = positive/negative by pnn. The line indicates
> the cut-off that I was expecting the model to guess.
> Many thanks
> Luigi
>
>>>>
> x <- c(3.15,    2.97,    3.21,    45,    2,    2.47,    2.97,    2.6,
>   7.35,    4.11,    37.12,    2.73,    36.36,    2.4,    2.74,    45,
>   2.47,    37.4,    45,    2.97,    2,    2,    2.55,    2.51,
> 2.68,    2.31,    2.6,    2,    2.57,    37.05,    13.84,    19.18,
> 21.94,    28.61,    38.01,    38.24,    38.33,    29.01,    24.64,
> 10.03,    10.12,    10.29,    10.32,    10.39,    10.41,    10.44,
> 10.51,    10.64,    10.65,    10.67,    10.83,    10.85,    10.97,
> 11.24,    11.43,    11.85,    11.87,    12.02,    12.03,    12.05,
> 12.12,    12.22,    12.29,    12.3,    12.33,    12.62,    12.62,
> 12.64,    12.69)
> y <- c(0.014,    0.008,    0.008,    0.001,    0.002,    0,    0.013,
>   0.008,    0.001,    0.011,    0.076,    0.005,    0.045,    0.002,
>  0.016,    0.001,    0.002,    0.086,    0.002,    0.019,    0,
> 0.002,    0.024,    0.015,    0.009,    0.013,    0.017,    0.009,
> 0.012,    0.088,    0.129,    0.097,    0.085,    0.096,    0.087,
> 0.103,    0.066,    0.11,    0.11, 0.001,    0.002,    0.002,
> 0.104,    0,    0.003,    0.116,    0.001,    0.002,    -0.001,
> 0.116,    0.124,    0.004,    0.116,    0.124,    0.119,    0.003,
> 0.112,    0.003,    0.002,    0.092,    0.118,    0.108,    0.104,
> 0,    0.112,    0.131,    0.001,    0.125,    0.005)
> z <- c(0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    1,
>   0,    1,    0,    0,    0,    0,    1,    0,    0,    0,    0,    0,
>    0,    0,    0,    0,    0,    0,    1,    1,    1,    1,    1,
> 1,    1,    1,    1,    1, 0,    0,    0,    1,    0,    0,    1,
> 0,    0,    0,    1,    1,    0,    1,    1,    1,    0,    1,    0,
>  0,    1,    1,    1,    1,    0,    1,    1,    0,    1,    0)
> t.df <- data.frame(z, x, y)
>
> t.pos <- subset(t.df, z == 1)
> t.neg <- subset(t.df, z == 0)
> plot(t.pos\$y ~ t.pos\$x,
>      col = "red", xlab="x", ylab="y",
>      xlim = c(min(t.df\$x), max(t.df\$x)),
>      ylim = c(min(t.df\$y), max(t.df\$y))
> )
> points(t.neg\$x, t.neg\$y)
>
> x <- c(38.01,    2.7,    4.89,    2.76,    2.96,    2.91,    38.61,
> 2.89,    2.07,    2.72,    2.77,    4.49,    3.06,    3.1,    2,
> 2.95,    3.37,    4.7,    2.98,    2.89,    44.6,    3.09,    28.05,
>  2.8,    4.76,    4.91,    3.04,    2.79,    3.1,    37.62,    5.49,
>  3.17,    4.53,    2.77,    2.87,    4.91,    3.08,    3.04,    3.03,
>   3.09,    4.74,    2.74,    4.25,    3.31,    28.22,    3.05,
> 4.68,    4.8,    3.12,    2.65,    2.62,    2.91,    38.32,    2.86,
>  2.96,    2.95,    16.24,    3.01,    3.25,    2.93,    2.92,    2.93,
>    2.99,    4.79,    3.13,    3.01,    3.29,    2.76,    3.44,
> 4.91,    3.14,    2.9,    3.03,    2.51,    2.91,    2.52,    45,
> 3.15,    44.48,    3.03,    2.76,    4.81,    14.97,    2.8, 12, 20,
> 25, 30)
> y <- c(0.082,    0.007,    0.034,    0.007,    0.027,    0.009,
> 0.057,    0.028,    0.007,    0.02,    0.022,    0.021,    0.012,
> 0.018,    0,    0.021,    0.041,    0.021,    0.021,    0.011,
> 0.025,    0.011,    0.102,    0.016,    0.035,    0.015,    0.008,
> 0.017,    0.028,    0.084,    0.013,    0.032,    0.004,    0.006,
> 0.025,    0.019,    0.006,    0.018,    0.019,    0.02,    0.021,
> 0.009,    0.015,    0.023,    0.089,    0.023,    0.025,    0.034,
> 0.035,    0.009,    0.006,    0.007,    0.056,    0.025,    0.016,
> 0.012,    0.101,    0.019,    0.017,    0.031,    0.019,    0.014,
> 0.044,    0.02,    0.018,    0.017,    0.018,    0.008,    0.02,
> 0.017,    0.016,    0.021,    0.02,    0.009,    0.019,    0.006,
> 0.002,    0.012,    0.016,    0.013,    0.016,    0.013,    0.101,
> 0.027, 0.01, 0.02, 0.03, 0.025)
> q.df <- data.frame(x, y)
> points(q.df\$x, q.df\$y, col="green")
>
> library(pnn)
> train <- learn(t.df[,1:3])
> fit <- smooth(train)
> # guess
> n <- nrow(q.df)
> Q <- rep(-1, n)
> for (i in 1:n) {
>     print(i)
>     Q[i] <- guess(fit, as.matrix(q.df[i,1:2]))\$category
> }
> R <- data.frame(q.df, Q, stringsAsFactors = FALSE)
>
> P <- subset(R, Q == 1)
> N <- subset(R, Q == 0)
> points (P\$x, P\$y, pch=5, col = "red")
> points (N\$x, N\$y, pch=5, col = "black")
> abline(h=0.035)
>
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