Package {kronxNBC}

kronxNBC: Clock of Regimes Naive Bayes Classifier (Student-t)

Description

Computes and fits a heavy-tailed Student-t Naive Bayes classifier for non-stationary financial market regime analysis (Clock of Regimes, COR). The core innovation is a profile grid search over the degrees-of-freedom parameter nu that prevents numerical underflow and structural classification failures when identifying fat-tailed Stress regimes. Provides S3 methods for fitting, prediction, summarising, plotting, and parameter extraction.

Author(s)

Maintainer: Oscar Linares olinares@umich.edu

Authors:

• Oscar Linares olinares@umich.edu

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

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

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

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

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

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

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

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)