Package 'kronxNBC'

Coefficient extraction for student_t_naive_bayes

Description

Returns a data frame of fitted Student-t parameters ($\mu$, $\sigma$, $\nu$) organised by feature (rows) and class (column groups).

Usage

## S3 method for class 'student_t_naive_bayes'
coef(object, ...)

Arguments

object	A fitted "student_t_naive_bayes" object.
...	Additional arguments (currently unused).

Value

A data frame with $p$ rows (features) and $3K$ columns, named <class>:mu, <class>:sd, <class>:nu for each of the $K$ classes.

See Also

student_t_naive_bayes

Examples

set.seed(7)
X <- matrix(rnorm(120), 60, 2, dimnames = list(NULL, c("f1", "f2")))
y <- factor(rep(c("A", "B", "C"), 20))
m <- student_t_naive_bayes(X, y)
coef(m)

---

Plot method for student_t_naive_bayes

Description

Draws per-feature Student-t density curves, one curve per class, for a fitted "student_t_naive_bayes" model.

Usage

## S3 method for class 'student_t_naive_bayes'
plot(
  x,
  which = NULL,
  ask = FALSE,
  legend = TRUE,
  legend.box = FALSE,
  arg.num = list(),
  prob = c("marginal", "conditional"),
  ...
)

Arguments

x	A fitted "student_t_naive_bayes" object.
which	Integer or character vector selecting which features to plot. NULL (default) plots all features.
ask	Logical. If TRUE the user is prompted before each plot. Default: FALSE.
legend	Logical. If TRUE (default) a legend is added to each plot.
legend.box	Logical. If TRUE the legend is drawn with a box. Default: FALSE.
arg.num	Named list of graphical parameters (e.g. col, lty) applied to the density lines. Defaults: sequential integer colours and solid lines.
prob	Character string: "marginal" (default) scales each density by the class prior; "conditional" plots the raw conditional density.
...	Additional graphical arguments passed to plot.

Value

Invisibly returns NULL.

See Also

student_t_naive_bayes

---

Predict method for student_t_naive_bayes

Description

Computes MAP class assignments or posterior probabilities for new observations using a fitted student_t_naive_bayes model.

Usage

## S3 method for class 'student_t_naive_bayes'
predict(
  object,
  newdata = NULL,
  type = c("class", "prob"),
  threshold = 0.001,
  eps = 0,
  ...
)

Arguments

object	A fitted "student_t_naive_bayes" object.
newdata	Optional numeric matrix of new observations with the same named columns as the training matrix. If NULL the training data stored in object are used.
type	Character string: "class" (default) returns a factor of predicted class labels; "prob" returns a numeric matrix of posterior probabilities (rows = observations, columns = classes).
threshold	Minimum log-density floor applied after the eps check. Prevents $-\infty$ contributions from absorbing the posterior. Default: 0.001.
eps	Densities at or below this value are replaced by threshold. Set to 0 (default) to use the machine minimum.
...	Additional arguments (currently unused).

Value

type = "class"

A factor of length nrow(newdata) with levels matching the training classes.

type = "prob"

A numeric matrix with nrow(newdata) rows and one column per class, containing softmax-normalised posterior probabilities.

See Also

student_t_naive_bayes

Examples

set.seed(1)
X <- matrix(rnorm(100), 50, 2, dimnames = list(NULL, c("f1", "f2")))
y <- factor(rep(c("A", "B"), 25))
m <- student_t_naive_bayes(X, y)
predict(m, type = "class")
predict(m, type = "prob")

---

Print method for student_t_naive_bayes

Description

Prints a concise summary of the model, including the call, prior probabilities, and the first five parameter tables.

Usage

## S3 method for class 'student_t_naive_bayes'
print(x, ...)

Arguments

x	A fitted "student_t_naive_bayes" object.
...	Additional arguments (currently unused).

Value

Invisibly returns x.

See Also

student_t_naive_bayes, summary.student_t_naive_bayes

---

Student-t Naive Bayes Classifier

Description

Fits a Naive Bayes classifier where the per-class, per-feature likelihood is a scaled Student-t distribution. The degrees-of-freedom parameter $\nu$ is selected for every (class, feature) pair by a profile log-likelihood grid search over nu_grid, making the model robust to the fat-tailed returns that characterise financial Stress regimes.

Usage

student_t_naive_bayes(x, y, prior = NULL, nu_grid = c(3:30, 40, 60, 100), ...)

Arguments

x	A numeric matrix of predictors with named columns. Each column is one feature; each row is one observation.
y	A factor, character, or logical vector of class labels with length equal to nrow(x). Must contain at least two distinct classes and at least two observations per class.
prior	Optional named numeric vector of prior class probabilities. Length must equal the number of class levels. Defaults to empirical class frequencies. Supplied values are normalised to sum to one.
nu_grid	Numeric vector of candidate degrees-of-freedom values used by the profile grid search. All values must be strictly greater than 2 (finite-variance requirement). Default: c(3:30, 40, 60, 100). Values near 3 capture extreme kurtosis typical of Stress regimes. Values near 30+ approximate Gaussian behaviour for Calm regimes. Including 60 and 100 provides a near-Gaussian safety net without imposing normality.
...	Additional arguments (currently unused).

Details

**Classification rule (MAP)**

Under the Naive Bayes conditional-independence assumption the posterior log-odds reduce to the Maximum A Posteriori rule:

$\hat{k} = \arg\max_{k \in \{1,\dots,K\}} \Bigl[ \log \pi_k + \sum_{j=1}^{p} \log f_{t}\!\left(x_j \,\Big|\, \mu_{kj},\, \sigma_{kj},\, \nu_{kj}\right) \Bigr]$

where the scaled Student-t density is

$f_{t}(x \mid \mu, \sigma, \nu) = \frac{1}{\sigma}\, f_{t_\nu}\!\!\left(\frac{x - \mu}{\sigma}\right)$

and $\pi_k$ is the prior probability of class $k$.

**Degrees-of-freedom grid search**

For each (class $k$, feature $j$) pair the algorithm runs one IRLS step at every candidate $\nu \in$ nu_grid and retains the triplet $(\hat\mu, \hat\sigma, \hat\nu)$ that maximises the profile log-likelihood. This discrete search avoids the numerical instability of continuous $\nu$ optimisation and is the mechanism that prevents log-likelihood underflow when scoring crisis observations in the Stress regime.

Value

An S3 object of class "student_t_naive_bayes" with components:

data

List with elements x (training matrix) and y (training labels).

levels

Character vector of class levels.

params

Named list with $K \times p$ matrices mu, sd, and nu ($K$ = classes, $p$ = features).

prior

Named numeric vector of prior probabilities.

nu_grid

The nu_grid vector used during fitting.

call

The matched call.

See Also

predict.student_t_naive_bayes, tables.student_t_naive_bayes, coef.student_t_naive_bayes

Examples

set.seed(42)
n  <- 150
y  <- factor(rep(c("Calm", "Stress", "Trend"), each = n / 3))
X  <- matrix(
  c(rnorm(50, 0, 1), rt(50, df = 4), rnorm(50, 1, 0.5),
    rnorm(50, 0, 1), rt(50, df = 4), rnorm(50, 1, 0.5)),
  nrow = n, ncol = 2,
  dimnames = list(NULL, c("ret", "vol"))
)
model <- student_t_naive_bayes(X, y)
print(model)

---

Summary method for student_t_naive_bayes

Description

Prints a high-level summary of a fitted "student_t_naive_bayes" model: sample size, feature count, $\nu$ grid range, and prior probabilities.

Usage

## S3 method for class 'student_t_naive_bayes'
summary(object, ...)

Arguments

object	A fitted "student_t_naive_bayes" object.
...	Additional arguments (currently unused).

Value

Invisibly returns object.

See Also

student_t_naive_bayes, print.student_t_naive_bayes

---

Parameter tables for Naive Bayes classifiers

Description

S3 generic that returns per-feature parameter tables for a fitted Naive Bayes model. For "student_t_naive_bayes" objects each table contains the fitted $\mu$, $\sigma$, and $\nu$ parameters. For all other model classes the call is forwarded to naivebayes::tables().

Usage

tables(object, which = NULL, ...)

## S3 method for class 'student_t_naive_bayes'
tables(object, which = NULL, ...)

## Default S3 method:
tables(object, which = NULL, ...)

Arguments

object	A fitted Naive Bayes model. Supported classes: "student_t_naive_bayes" (this package) and any class accepted by tables.
which	Integer or character vector selecting which feature tables to return. NULL (default) returns all features.
...	Additional arguments passed to the method.

Value

A "naive_bayes_tables" object: a named list with one element per selected feature. For "student_t_naive_bayes" objects each element is a table with rows mu, sd, nu and one column per class level.

See Also

tables, student_t_naive_bayes

Examples

set.seed(3)
X <- matrix(rnorm(120), 60, 2, dimnames = list(NULL, c("ret", "vol")))
y <- factor(rep(c("Calm", "Stress", "Trend"), 20))
m <- student_t_naive_bayes(X, y)
tables(m)
tables(m, which = "ret")
tables(m, which = 2L)

---