Using Custom Kernels with FastSurvivalSVM: The Wavelet Kernel

Introduction

The FastSurvivalSVM package provides an efficient R interface to the Python class FastKernelSurvivalSVM from the scikit-survival library.

A powerful feature of this package is the ability to define fully custom kernel functions in R. Previously, this required complex programming patterns (function factories and closures). Now, with the helper function grid_kernel(), defining and using a custom kernel is straightforward.

This vignette demonstrates:

How to define a custom kernel using simple R syntax.
How to instantiate a specific kernel version using grid_kernel().
How to fit a model using the wavelet kernel (Ará et al., 2016).
How to extract predictions, C-index, coefficients, and hyperparameters.

Data Example

We begin by generating a synthetic survival dataset with nonlinear relationships to test the kernel’s capability.

library(FastSurvivalSVM)

# Function to generate synthetic survival data
data_generation <- function(n, prop_cen) {
    x1 <- rnorm(n, 1, 1)
    x2 <- rnorm(n, 2, 2)
    x3 <- rexp(n)
    
    xbeta <- x1 * log(abs(x2)) + 2 * sin(x3 - x2)^2
    shape <- 2
    scale <- 5
    
    u <- runif(n, 0, 1)
    time_t <- ((-log(1 - u))^(1 / shape)) * scale * exp(-xbeta)
    
    ind_cens <- sample(1:n, n * prop_cen, replace = FALSE)
    time_gerado <- time_t
    time_gerado[ind_cens] <- runif(
        length(ind_cens),
        min(time_t),
        time_t[ind_cens]
    )
    
    cens <- rep(1, n)
    cens[ind_cens] <- 0

    data.frame(
        tempo = time_gerado,
        cens  = cens,
        x1    = x1,
        x2    = x2,
        x3    = x3
    )
}

set.seed(123)
df <- data_generation(n = 300L, prop_cen = 0.1)

head(df)
#>         tempo cens        x1         x2         x3
#> 1   1.4801101    1 0.4395244  0.5695156 0.33901239
#> 2   2.3390461    1 0.7698225  0.4946221 0.43618362
#> 3 788.5807128    1 2.5587083  0.1229226 0.73802924
#> 4  17.1329416    1 1.0705084 -0.1050266 0.57069724
#> 5   1.6826516    1 1.1292877  1.1256809 0.08437658
#> 6   0.0492852    1 2.7150650  2.6623583 1.35933656

Wavelet Kernel Implementation

The wavelet kernel described in Ará et al. (2016) uses the following mother function:

$h(u) = \cos(1.75u) e^{-u^2 / 2}$

And the kernel is defined as the product over covariates:

$K(x, z) = \prod_{k=1}^p h\left( \frac{x_k - z_k}{A} \right)$

1. Defining the Kernel Function

wavelet_kernel_fn <- function(x, z, A = 1) {
  x <- as.numeric(x)
  z <- as.numeric(z)
  u <- (x - z) / A
  prod(cos(1.75 * u) * exp(-0.5 * u^2))
}

2. Instantiating the Kernel

my_wavelet <- grid_kernel(wavelet_kernel_fn, A = 0.5)
class(my_wavelet)
#> [1] "fastsvm_custom_kernel" "function"

Fitting the Model

fit_wavelet <- fastsvm(
  data          = df,
  time_col      = "tempo",
  delta_col     = "cens",
  kernel        = my_wavelet,
  alpha         = 1,
  rank_ratio    = 0,
  fit_intercept = FALSE
)

Predictions

preds <- predict(fit_wavelet, df)
head(preds)
#> [1]  1.4810330  1.6302696 49.1482327  5.0829020  1.1056405  0.1682349

Concordance Index (C-index)

c_index <- score(fit_wavelet, df)
cat(sprintf("C-index on training data: %.4f\n", c_index))
#> C-index on training data: 0.9373

Model Summary

summary(fit_wavelet)
#> Summary of FastKernelSurvivalSVM model (kernel survival SVM)
#> ======================================================================
#> 
#> == Data ==
#> - n (observations) : 300
#> - p (covariates)   : 3
#> - Covariates       :  x1, x2, x3 
#> 
#> == Hyperparameters ==
#> - kernel           : custom callable function
#> - alpha            : 1
#> - rank_ratio       : 0 (0 = pure regression)
#> - fit_intercept    : FALSE
#> 
#> == Estimated parameters (coef_ = sample-wise weights alpha_i) ==
#> - Number of support-like vectors (|alpha_i| > 1e-8): 282
#> - Summary of alpha_i (coef_):
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> -2.15467 -0.59048  0.00000 -0.04655  0.42036  4.91534 
#> 
#> - Number of optimization iterations: 14
#> ======================================================================

Extracting Coefficients and Parameters

head(coef(fit_wavelet))
#> [1] -0.0006233144  0.3609977816  2.7753938725  1.2151206510  0.4199461135
#> [6] -1.2277373095
get_params_fastsvm(fit_wavelet)
#> $alpha
#> [1] 1
#> 
#> $coef0
#> [1] 1
#> 
#> $degree
#> [1] 3
#> 
#> $fit_intercept
#> [1] FALSE
#> 
#> $gamma
#> NULL
#> 
#> $kernel
#> <function make_python_function.<locals>.python_function at 0x11d657d80>
#>  signature: (*args, **kwargs)
#> 
#> $kernel_params
#> NULL
#> 
#> $max_iter
#> [1] 20
#> 
#> $optimizer
#> [1] "rbtree"
#> 
#> $random_state
#> NULL
#> 
#> $rank_ratio
#> [1] 0
#> 
#> $timeit
#> [1] FALSE
#> 
#> $tol
#> NULL
#> 
#> $verbose
#> [1] FALSE

Conclusion

This vignette demonstrated the streamlined workflow for custom kernels in FastSurvivalSVM.

Pedro Rafael Diniz Marinho

2026-01-26