# A novel RNA pseudouridine site prediction model using utility kernel and
data driven parameters

Sourabh Patil
Dept. of Biological Sciences, BITS Pilani K K Birla Goa Campus, Goa, India
<EMAIL_ADDRESS>&Archana Mathur
Dept. of Information Science and Engineering, Nitte Meenakshi Institute of
Technology, India
<EMAIL_ADDRESS>&Raviprasad Aduri
Dept. of Biological Sciences, BITS Pilani K K Birla Goa Campus, Goa, India
<EMAIL_ADDRESS>&Snehanshu Saha
Dept. of CSIS and APPCAIR, BITS Pilani Goa, India
HappyMonk AI, Bangalore, India
<EMAIL_ADDRESS>
###### Abstract

RNA protein Interactions (RPIs) play an important role in biological systems.
Recently, we have enumerated the RPIs at residue level and have elucidated the
minimum structural unit (MSU) in these interactions to be a stretch of five
residues (Nucleotides/amino acids). Pseudouridine is the most frequent
modification in RNA. The conversion of uridine to pseudouridine involves
interactions between pseudourdine synthase and RNA. The existing models to
predict the pseudouridine sites in a given RNA sequence mainly depend on user
defined features such as mono and dinucleotide composition/propensities of RNA
sequences. Predicting pseudouridine sites is a non-linear classification
problem with limited data points. Deep Learning models are efficient
discriminators when the data set size is reasonably large and fails when there
is paucity in data ($<1000$ samples). To mitigate this problem, we propose a
Support Vector Machine (SVM) Kernel based on utility theory from Economics,
and using data driven parameters (i.e. MSU) as features. For this purpose, we
have used position-specific tri/quad/pentanucleotide composition/propensity
(PSPC/PSPP) besides nucleotide and dineculeotide composition as features. SVMs
are known to work well in small data regime and kernels in SVM are designed to
classify non-linear data. The proposed model outperforms the existing state of
the art models significantly ($10\%-15\%$ on average).

_K_ eywords pseudouridine $\cdot$ RNA protein interactions $\cdot$ Utility
Kernel (UK) $\cdot$ Small data Machine learning (ML)

##  1 Introduction

Pseudouridine ($\psi$) is a modified nitrogenous base commonly found in RNA.
It is formed by the isomerization of uridine, a natural RNA building block, to
provide structural and functional diversity. $\psi$ is present in transfer RNA
(tRNA), ribosomal RNA (rRNA), and small nuclear RNA (snRNA) among other types
of RNA [2]. $\psi$ sites are highly conserved across different species,
indicating their functional significance. The discovery and characterization
of $\psi$ sites have been facilitated by advances in high-throughput
sequencing technologies and computational approaches. These techniques enable
researchers to map and identify $\psi$ sites on a global scale, providing
insights into their distribution and functional roles across various RNA
molecules. Understanding the role of $\psi$ sites in RNA biology continues to
be an active area of research with potential implications for various fields,
including molecular biology, genetics, and medicine. Finding $\psi$ sites in
RNA is desirable for several reasons:

  * •

Understanding RNA modification: Understanding RNA post-transcriptional
modifications enables researchers to unravel the regulatory mechanisms that
control RNA processing, stability, and function.

  * •

RNA structure and function: Role of $\psi$ modifications contribute to RNA
folding, stability, and interactions with other molecules. This knowledge
helps elucidate the molecular mechanisms underlying RNA-mediated processes
such as translation, splicing, and RNA-protein interactions.

  * •

Biomarker discovery: Discovering $\psi$ sites can lead to the identification
of potential RNA biomarkers associated with specific physiological conditions
or pathologies.

  * •

Evolutionary conservation: Comparative studies of $\psi$ sites can shed light
on the evolutionary relationships between species and help decipher the
functional consequences of $\psi$ modifications in different biological
contexts.

  * •

RNA-targeted therapies: The discovery of $\psi$ sites can aid the development
of RNA-targeted therapies. RNA modifications, including pseudouridine, can
influence the efficacy and specificity of RNA-targeting drugs, such as
antisense oligonucleotides or mRNA-based vaccines.

Recently, $\psi$ site prediction using AI tools has gained prominence owing to
the above mentioned reasons.The performance of these methods are far from
ideal given the advancements in both AI tools and biological data
representation. Pseudouridylation of RNA involves the structural context of
both the protein and RNA. One major contributing factor for a functional RNA
protein interaction is the structural context of the two partners [12, 6]. All
the existing methods are agnostic to the structural features of RNA while
representing the data. Our recent work on predicting RNA protein interactions
(RPI) revealed the presence of a minimum structural unit (MSU) in RPI [8].
This MSU consists of a stretch of five nucleotides/amino acids in RNA/protein
for a stable interaction to occur between the two partners. Based on this
knowledge, we have used position specific tri, quad, and penta nucleotide
propensities besides the mono and di nucleotide compositions as features and
utility kernel, here we propose an SVM model for predicting $\psi$ sites in
RNA.

##  2 Related Work/Contributions:

There are two existing methodologies viz iRNA-PseU [4] and PseUI [7]. The
iRNA-PseU had Nucleotide density and pseudo-nucleotide composition (PseKNC) as
features.

On the other hand, the PseUI had five different features in their work -
Nucleotide composition, Dinucleotide composition, Position-specific nucleotide
propensity (PSNP), Position-specific dinucleotide propensity (PSDP), and
PseKNC. They used the RBF kernel of the Support vector machine (SVM) to solve
the challenge of predicting the RNA pseudouridine site.

The best performance these methods could achieve is an accuracy of around 70 %
auguring for improving the existing state of the art. To improve any ML based
model, one needs to consider the feature representation and the ML
architecture. Herein, we have proposed RNA features based on the knowledge
derived from our RPI work [8] and by taking a cue from the utility kernel
applied in the domain of economics. We refer to our model as ’PSe-MA’.

###  2.1 Our Contributions

  1. 1.

For any prediction model that involves structural context of a given
biomolecule, as is the case with $\psi$ site prediction in RNA, we propose
using data driven parameters as well as the minimum structural unit (MSU) of
the given biomolecule as one of the features.

  2. 2.

We present the insight into the Small Sample Size ($S^{3}$) classification
problem as the key driving point behind our data-driven investigation as we
noticed that the baseline models that used SVM RBF kernels didn’t provide any
justification!

  3. 3.

The insight (refer figure 1) leads to the discovery of a novel SVM Kernel. We
propose a parameterized utility kernel for the task presented in this work.

  4. 4.

We empirically validated the discrimination ability of the kernel and showed
that it outperforms the previous baseline and other ML algorithms by a
significant margin.

  5. 5.

Further, We present the Mathematical and computational foundation of the novel
Kernel which explains the superior performance.

##  3 Methods

This study used three benchmark datasets for training: H990, S628, and M944. A
datailed description of each of them can be found in the ’Data’ section below.
These are the same datasets used by iRNA-PseU and PseUI methods. These
datasets are curated from the experimentally found $\psi$ sites from RMBase
for H. sapiens, M. musculus, and S. cerevisiae. The negative dataset is made
of RNA sequences that were experimentally confirmed to not have $\psi$ sites.
For more detailed information on how these datasets were constructed, refer to
[4]. Each of the datasets has equal number of positive and negative samples
(i.e. RNA sequences with and without a pseudouridylation site). For example,
H990 contains 495 sequences with a $\psi$ site and 495 sequences with uridine
that doesn’t get pseudouridylated. We denote each RNA segment as
$R_{\epsilon}$(U), in these datasets as:
$R_{\epsilon}$(U)=$N_{-\epsilon}N_{-(\epsilon-1)}.....N_{-1}UN_{1}....N_{(\epsilon-1)}N_{\epsilon}$
where the center U represents ‘uridine’, $N_{\epsilon}$ represents the
$\epsilon$-th upstream nucleotide from the central uridine and N+$\epsilon$
represents the $\epsilon$-th downstream nucleotide. The RNA samples in H990
and M944 are composed of 21 nucleotides each, while those in S628 consist of
31 nucleotides. Hence, the $\epsilon$ is 10, and the RNA segment length is 2 ×
10 + 1 for the H900 and M944 datasets. The value of $\epsilon$ is 15, and the
RNA segment length is 2 × 15 + 1 for the S628 dataset. In addition to the
training datasets, we have used two independent testing datasets, namely H200
and S200, provided by Chen et al. [4] for validation.

###  3.1 Feature representation of RNA samples

Encoding an RNA sequence as a feature vector with highly discriminative
features is one of the main challenges in building a predictor based on
machine learning. This is due to the fact that all currently available machine
learning methods can only handle vectors with identical lengths for all
sequence samples. A vector formed in a discrete paradigm, however, can lose
its sequence-pattern details. Here, we propose five different features to
represent the RNA sequences: nucleotide composition (NC); dinucleotide
composition (DC); position-specific trinucleotide propensity (PSTP); position-
specific quadnucleotide propensity (PSQP); and position-specific
pentanucleotide propensity (PSPP, which is also the MSU for RNA) features. The
NC and DC are calculated using the the Pse-in-One server [10]. Below is a
brief description of the features used in the current study.

  * •

Nucleotide composition (NC): NC refers to the frequencies of each nucleotide
(A, U, G, and C) within a sequence or a specific region of interest.

  * •

Dinucleotide composition (DC): DC, also known as di-nucleotide frequency or
di-nucleotide content, is a feature commonly used in computational biology to
take advantage of the context dependence of the nucleotides (i.e. the
presence/absence of a specific nucleotide either on the 5´or the 3´side of the
given nucleotide.

  * •

Position-specific trinucleotide propensity (PSTP): PSTP provides a measure of
the effect of nearest neighbors in the axiom of sequence to structure to
function. Instead of accounting for either the upstream or downstream
nucleotide identity as done in DC, herein, one can incorporate the information
of both the up and downstream nucleotide identity for a given nucleotide at a
given position in the sequence. This provides a basic measure of the
structural context of each of the nucleotides in the RNA sequence.

  * •

Position-specific quadnucleotide propensity (PSQP): PSQP expands upon the PSTP
in terms of the number of nearest neighbors being considered for the feature
generation. The tetra nucleotide composition is considered here based on the
knowledge, from the literature and our work on RPIs involved in alternative
splicing, that most of the RNA sequence motifs that recognise/involved in the
RPIs are of four nucleotides in length [11].

  * •

Position-specific pentanucleotide propensity (PSPP): The final feature we have
constructed for this study is the PSPP. In the case of biomolecular
interactions, for example RPI, the structure dictates the interaction. In case
of RNA, the minimum structural unit, the hairpin structure, is of five
nucleotides. Our previous studies on RPI enumeration also revealed the MSU to
be of five nucleotides. Hence, we have constructed the PSPP feature to keep
the structure information of the given RNA sequences intact.

##  4 RNA pseudouridine site prediction: The ML Challenge

Data: As shown in the tables (see supplementary file, section D tables 7-8),
three datasets were used in this study corresponding to species H.sapiens,
S.cerevisiae and M.musculus respectively. It is a binary balanced
classification problem with an equal number of positive and negative samples.
Class 1 corresponds to the RNA sequences which have a pseudouridine site
present in them and Class 0 corresponds otherwise. Therefore, RNA
pseudouridine site prediction is a supervised machine learning
(classification) problem. In addition to the training datasets, Chen et al.
[4] provided two independent testing datasets for H. sapiens and S.
cerevisiae, namely H200 and S200, but not for M. musculus.

Deep Learning models fail to perform well when the sample size is small [15]
[9], particularly when the samples are less than a thousand. Additionally, if
the data is non-linear in nature, the classification tasks become even more
challenging. Deep Learning models efficiently discriminate non-linear decision
surfaces if and only if the models are trained on sufficiently large data as
they can generate new features from the corpus of data and find separating
hyperplanes. The notion of being able to approximate data patterns via the
Universal approximation theorem [16] also rests on this assumption. Therefore,
the choice of a suitable Machine Learning (ML) model is restricted to the ones
that are not data-hungry! Support Vector Machines (SVM) is one such robust ML
model grounded on sound statistical learning theory, effectively operating in
the small sample regime (known as small sample size or $S^{3}$ problems). They
are known to perform well on linear (linear-SVM) as well as non-linearly
separable datasets (SVM kernels) (refer figure 1). The idea behind SVM kernels
is to transform the training data into higher dimensional space and find an
optimal hyperplane that separates the data into distinct classes. In the
language of computational learning theory, these attributes are known as
Universal Approximation power, Generalization ability, Error bounds, and VC
Dimensions.

Figure 1: Feature-feature plots of the dataset (RNA pseudouridine site
prediction): non-linear decision surface is clearly visible i.e. linear
model/surface can’t separate (shatter) the red points from the blue ones.

###  4.1 Solution: Our SVM kernel Model

Based on the property of inner product, which can be extended to a Hilbert
Space produces $\langle x,y\rangle=x_{1}y_{1}+x_{2}y_{2}$, we adapted a class
of utility functions, novel kernel, to the properties of the inner product. In
general, a direct (or indirect) utility function with the display of
properties such as reflexivity, monotonicity can be classified within the
broad range of von Neumann Morgenstern (sequence of) utility functions [5]
with point-wise convergence or with almost anywhere convergence. This paper
utilizes the inner products in lieu of utility functions preserving existing
characteristics including the uniqueness of optimal choices supported by
budget constraints that are also inner products in the price and commodity
space. Suppose, the budget set facing a consumer is given by:
$Bp_{w}=\\{x|px\leq w\\}$ where, $w=$ income or wealth; the budget frontier
(line or hyperplane) is given by $\overline{B}=\\{x|px=w\\}.$ If $p$ is
orthogonal to a budget frontier $\overline{B}$, then if, $x,y\in\overline{B}$
, then the inner product is $p(y-x)$, where, $p(y-x)=py-px=w-w=0$. We leverage
these ideas to construct a Utility kernel for classification. Von Neumann-
Morgenstern utility functions the degree of risk aversion (in the case of
Hyperbolic Absolute Risk Aversion (HARA) [13], it is the risk tolerance
instead) can classify elements according to distinct risk-taking abilities,
ex-post. In all unconstrained cases, the utility function itself may operate
as the classifier. Indeed, in this case, the utility functions are raised to
power with the help of a risk aversion parameter, which can well be a (non-
zero) integer used as a scaling factor, or restricted between zero and one, in
order to obtain a classification. This sets the ground for our Utility Kernel,
The Utility Kernel: We propose a Utility kernel, expressed as:

$K(x_{i},x_{j})=k_{0}+k_{1}<x_{1},x_{2}>^{\alpha}$ (1)

where $k_{0},k_{1}$ are tunable parameters and $\alpha$ is the degree of the
proposed kernel.

###  4.2 The Mathematical foundation of Utility kernel: Generalization
ability, Error bounds and VC Dimensions

We state some important theoretical findings related to the utility kernel.
The proofs are available on request. These results provide the foundation for
the utility kernel (UK) in the sense that they state (1) why the utility inner
product qualifies as an SVM kernel (Mercer’s Theorem), (2) how good is the
approximation capability of the UK on the trained samples (UK as universal
approximator), (3) performance on the unseen test data (Generalization
ability, Error bounds) and (4) the ability of UK to shatter (classify) the
largest set of points i.e. it is a measure of the capacity of a hypothesis set
to fit different data sets or the measure of the complexity of the UK model
and its fitting ability on different data sets (VC dimension). A Kernel must
satisfy Mercer’s theorem as follows.
Mercer’s Theorem: If $K$ is a continuous symmetric function such that the
integral operator $L_{K}:L^{2}\rightarrow L^{2}$, defined as $L_{K}g(x)=\int
K(x,y)g(y)dy$ is positive, then for all functions $g\in L^{2}$, the condition
$\int\int K(x,y)g(x)g(y)dxdy\geq 0$ stands true.
Utility kernel as universal approximator:
Theorem: A function $\mathfrak{F}$ can be called a universal approximator if,
for a compact set $C\subset\Re^{m}$, a continuous function h can be found such
that the maximum norm $\left|f(x)-h(x)\right|\leq\epsilon$ for
$f\in\mathfrak{F}$ and $\epsilon>0$. Let there be m-dimensional non-linearly
separable patterns $\left(x_{1},y_{1}\right)\cdots(x_{n},y_{n})$. Let
$\phi:\Re^{m}\rightarrow X$ be a non-linear mapping, where $X$ is a higher
dimensional Hilbert space, $w$ be the weight vector, $b$ be the bias, ’.’ be
the dot product, $\mathbf{H}$ be the Heaviside function,
$\mathbf{H}:\Re\rightarrow\left\\{-1,1\right\\}$. Assuming that we use utility
kernel to train the samples, after solving the Kuhn-Tucker conditions and the
dual optimization problem, we get a classifier of the form,

$x=\textbf{H}\left(\sum_{j}\alpha_{j}y_{y}k\left(x_{j},x\right)+b\right)$

where $\alpha_{j}$ is the Langrange multiplier, $x,x_{j}\in\Re$. Let
$C_{g}^{H}(k)$ be the general class of functions with arbitrary $\alpha_{j}$,
$x_{j}$ and b, k being the utility kernel.
Preposition: 4.1 The dimension of feature space of the utility kernel
$k_{u}(x_{1},x_{2})$ is

$dim(k_{u})=\left\\{\begin{matrix}\binom{n+d-1}{d}+1&ifd\neq n\\\
\frac{1}{2}\binom{n+d}{d}+1&otherwise\end{matrix}\right.$

Theorem: $\bigcup_{u=1}^{\infty}C^{\textbf{H}}(k_{u})$ possess the universal
approximation capabilities if the kernel $k_{u}$ is defined as

$k_{u}(x_{1},x_{2})=k_{0}+k_{1}\left(x_{1}\cdot x_{2}\right)^{u}$ (2)

The VC dimension of the Utility Kernel:
Valiant [18] proposed that any learning algorithm can find a hypothesis or
rule that approximates the best possible rule with some degree of probability.
Theorem: Assume training examples
$S=\left\\{x_{1},x_{2}...x_{l}\right\\}\in\Re^{d}$ when transformed by
function $\phi$, the space of the transformed features is bounded by smallest
hyper-sphere with radius $R$ and center $C$. The VC dimension $VC_{K}$ for the
Utility kernel $K(,)$ is bounded by the following inequality -

$VC_{K}\leq min\left(\left[\frac{R^{2}w^{2}}{4}\right],d\right)+1$

where
$R^{2}=K(x_{p},x_{p})-2\sum_{i=1}^{l}\beta_{i}K(x_{i},x_{p})+\sum_{j=1}^{l}\sum_{k=1}^{l}\beta_{j}\beta_{k}K(x_{j},x_{k})$
and
$<w,w>=\sum_{i=1}^{l}\sum_{j=1}^{l}\alpha_{i}\alpha_{j}y_{i}y_{j}K(x_{i},x_{j})$,
$\alpha_{i},\alpha_{j},\beta_{i},\beta_{j},\beta_{k}$ are the Lagrangian
multipliers. $\phi x_{p}$ is the farthest training sample lying on the
circumference of the hyper-sphere.The values are essentially data-dependent,
as we compute inner products of pairwise samples from the training set. We
computed the kernel parameters on the curated data.

##  5 Experimental Settings

We conducted our experiments on an Intel(R) Core(TM) i3-8145U laptop with 8GB
RAM. Python 3.10 was used to build the ML models and the Utility Kernel was
coded from scratch. The grid search was implemented to find the optimal
parameters of $k_{0}$, $k_{1}$, and $\alpha$. All experiments were run three
times and mean and standard deviation of accuracy and other metrics were
reported. Along with accuracy, sensitivity, and specificity, the Matthews
Correlation Coefficient (MCC), and Area Under the Curve (AUC) are reported for
each experimental run.

Validation techniques: Cross-validation (CV) techniques used in the ML domain
ensure that the trained model performs well on unseen data. The main idea
behind CV is to prevent the model from doing overly well during training but
performing miserably when tested in the new data (overfitting). The most
popular choices in CV techniques include jackknife, 66%-33% train-test split,
and k-fold cross-validation. Jackknife (aka Leave-one-out CV) takes the entire
dataset for training but leaves one sample for testing. The train-test batches
are created to train the model and the performance is averaged in the end.
This ensures a low bias in the results but the presence of an outlier may lead
to high variance. The 66%-33% train-test split is the standard way of CV where
66% of data is used for training and 33% of data is used for reporting the
performance of the model. In K-fold CV, the data is divided into K-folds. The
$k-1$ folds are used for training and the $k^{th}$ fold is tested, and the
process is repeated $k$ times, each time with a different subset for train and
test.

Robustness Settings: We run our method 3 times and report the average and
standard deviation of the performance metrics. This is done to ensure the
reproducibility of the results under identical settings. We expect minimum
statistical variance which should be the desired outcome. Additionally, we run
Bonferroni comparisons [1] which count the number of times a proposed method
turns out to be superior to the baselines and other methods. For example, in
order to claim a method as SOTA, it must display superior performance in the
majority of the runs (at least 3 out of 5, 6 out of 10 for instance). We
computed the Bonferroni Statistic for our method PSe-MA (on Utility Kernel).
The BC value for PSe-MA was 3 (out of 3) in all the datasets.

Performance Evaluation metrics: In classical ML, a confusion matrix adds a lot
of visibility while solving the classification problem, whether binary or
multi-class. While testing the model, the confusion matrix presents a count of
actual and predicted labels of the classifier. It outputs ”TN”, which is the
number of actual ’negative’ samples predicted as negative, and ”TP” indicates
the number of actual ’positive’ samples predicted as positive. ”FN” implies
positive samples wrongly predicted as negative and ”FP” indicates negative
samples wrongly predicted as positive. We have used 5 types of evaluation
metrics viz. sensitivity, specificity, accuracy, MCC, and AUC (Area under the
curve). Sensitivity is the ratio of true positives and the actual positives in
the data, given as, $Sensitivity=\frac{TP}{TP+FN}$. Specificity is the ratio
of true negatives to the total negatives of the model, represented as
$Specificity=\frac{TN}{TN+FP}$. Accuracy is the measure of correct predictions
from the total predictions. The formula is
$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$. MCC is the correlation between the
actual and predicted values of the classifier and is defined as,
$MCC=\frac{TP*TN-FP*FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$. AUC is obtained
from the ROC Curve by plotting sensitivity against 1 - specificity. AUC is
desired to be close to 1 for superior classification performance.

Generalization settings: The generalization setting is designed for a specific
test in mind. It is important to know the efficacy of a classifier trained on
one data set and be tested on a completely new data set with identical
features as the previously generated data. For this ’blind’ validation, there
are two separate datasets for H. sapiens and S. cerevisae each of them have
200 samples (100 positive and 100 negative) More details about these datasets
can be found in the supplementary text section D. The setting is different
from using a train-test-validate split used traditionally. Needless to
mention, Jackknife validation doesn’t apply in this setting.

PSe-MA (Utility kernel) using jack-knife CV with PseUI and iRNA-PseU models
---
Training datasets |  Model used |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  iRNA-PseU (rbf) |  61.01 |  59.80 |  60.40 |  0.21 |  0.64
|  iRNA-PseU (linear) |  63.56 |  60.21 |  61.01 |  0.31 |  0.34
|  iRNA-PseU (UK) |  66.21±0.02 |  59.98±0.09 |  61.92±0.05 |  0.34±0.01 |  0.55±0.008
|  PseUI (rbf) |  64.85 |  63.64 |  64.24 |  0.28 |  0.68
|  PseUI (linear) |  66.78 |  65.87 |  67.89 |  0.35 |  0.56
|  PseUI (UK) |  70.76±0.06 |  69.54±0.009 |  71.33±0.01 |  0.46±0.05 |  0.50±0.04
|  PSe-MA (rbf) |  70.71 |  81.21 |  75.96 |  0.52 |  0.76
|  PSe-MA (linear) |  78.38 |  84.44 |  81.41 |  0.63 |  0.81
|  PSe-MA (UK) |  90.04±0.06 |  91.14±0.03 |  90.60±0.09 |  0.84±0.01 |  0.90±0.02
S628 |  iRNA-PseU (rbf) |  64.65 |  64.33 |  64.49 |  0.29 |  0.81
|  iRNA-PseU (linear) |  65.64 |  67.66 |  67.64 |  0.39 |  0.63
|  iRNA-PseU (UK) |  68.55±0.001 |  69.33±0.02 |  68.61±0.09 |  0.51±0.06 |  0.89±0.08
|  PseUI (rbf) |  62.10 |  71.02 |  66.56 |  0.33 |  0.69
|  PseUI (linear) |  63.56 |  68.92 |  68.71 |  0.23 |  0.56
|  PseUI (UK) |  67.33±0.06 |  68.79±0.01 |  72.73±0.09 |  0.33±0.008 |  0.69±0.01
|  PSe-MA (rbf) |  91.05 |  94.60 |  92.83 |  0.86 |  0.93
|  PSe-MA (linear) |  91.37 |  95.56 |  93.47 |  0.87 |  0.93
|  PSe-MA (UK) |  98.49±0.06 |  98.49±0.05 |  98.41±0.07 |  0.97±0.01 |  0.98±0.08
M994 |  iRNA-PseU (rbf) |  73.31 |  64.83 |  69.07 |  0.38 |  0.75
|  iRNA-PseU (linear) |  74.43 |  63.31 |  66.32 |  0.41 |  0.71
|  iRNA-PseU (UK) |  79.87±0.01 |  60.81±0.08 |  70.34±0.05 |  0.41±0.009 |  0.75±0.06
|  PseUI (rbf) |  74.58 |  66.31 |  70.44 |  0.41 |  0.77
|  PseUI (linear) |  73.23 |  68.92 |  71.82 |  0.51 |  0.82
|  PseUI (UK) |  75.78±0.009 |  68.76±0.07 |  73.22±0.04 |  0.64±0.01 |  0.79±0.09
|  PSe-MA (rbf) |  77.69 |  77.38 |  77.35 |  0.56 |  0.79
|  PSe-MA (linear) |  80.51 |  81.57 |  81.04 |  0.62 |  0.81
|  PSe-MA (UK) |  95.40±0.04 |  95.40±0.03 |  94.73±0.009 |  0.89±0.02 |  0.94±0.05

Table 1: Jack-knife Cross-validation Results: iRNA-PseU and PseUI used RBF SVM
on their data; our method PSe-MA used Utility Kernel on new biological
features extracted in this work; the three feature vectors are made to run on
three SVM kernels viz. RBF, linear and utility kernel. Utility Kernel
outperformed the other methods with a Bonferroni Comparison (BC) value of 3.

##  6 Results and discussions

We evaluated the performance of different existing predictors with our
proposed method, PSe-MA, and carefully tabulated the results in this section
111 Tables of results, Code and Data Repository are at the github link. The
parameters $k_{0}$ and $k_{1}$ of the proposed kernel are optimized by using
the grid search technique. To investigate the performance of PSe-MA for $\psi$
site identification, the method is compared with the predictions from state-
of-the-art ML models like XGBoost [3], Random Forest [17], Decision Tree [14],
and Naïve Bayes [19]. Further, we incorporated the jackknife, 5-fold cross-
validation, and 66-33% CV (results of 5-fold CV and 66-33% CV in the
supplementary file, section A, B) techniques to ensure meticulous performance
validation across all the models. The brief description of the notations used
is as follows. PSe-MA is the proposed method with new feature vectors (refer
to section 3.1) which uses the proposed Utility kernel to predict $\psi$
sites. The other baselines - iRNA-PseU [4] and PseUI [7] used RBF kernel on
their own feature vectors. The derived features from each of the predictors
are empirically evaluated on different kernels - Linear, RBF, and Utility
Kernel. The cross-examination of features on these methods is presented to
explain the in-depth analysis of the contributions of Utility Kernel on $\psi$
site identification.

A different set of experiments involves a comparison of XGBoost, Random
Forest, Decision Tree, and Naïve Bayes with Utility Kernel on the newly
proposed features (of PSe-MA). Table 1, compares the performance of features
from iRNA-PseU, PseUI, and PSe-MA on RBF, linear, and Utility Kernel and,
table 2, compares the performance of Utility Kernel with XGBoost, Random
Forest, Decision Tree, and Naive Bayes on (only) PSe-MA features by using
jackknife CV. The results of the 5-fold CV and 66-33% CV are in the
supplementary file sections A, and B; tables 1-4. While performing the
experiments, the regularization parameter, C, and, the width parameter,
$\gamma$ of the RBF kernel are optimized via grid search. Correspondingly, the
$n\\_estimators$ for Random forest and Decision Tree were taken to be the
best-performing values. It is evident from the tables that PSe-MA (Utility
Kernel) has outperformed the standard baselines (iRNA-PseU, PseUI) and the
other competent ML models by a large margin for predicting the presence of
$\psi$ site in the RNA samples. As per the results listed in table 1, PSe-MA
is 32.2% and 28.8% more accurate than iRNA-PseU and PseUI respectively on the
H990 dataset, while it is 34.6% and 32.6% more accurate than iRNA-PseU and
PseUI on S628 dataset and its 26.9% and 25.5% more accurate than iRNA-PseU and
PseUI on M994 dataset for the task of $\psi$ site identification.
Results of Generalization Settings: Even under this novel setting, where the
train and validation data are designed to be completely different (so as to
completely overrule any possibility of leak validation), our method PSe-MA
(Utility Kernel) shows SOTA results outperforming all existing baselines. The
results are tabulated in Table 5 section B of the supplementary file where
PSe-MA gave 95.40% and 99.68% accuracy in the two datasets thus surpassing the
best accuracies from XGboost and Random Forest by a fair margin. It’s
important to note, however, that, the absolute performance is of lower
priority. The ability of the Utility Kernel to adapt to completely unseen data
and be able to generalize well is the pertinent point!

Different ML models on the three training datasets using PSe-MA (Jackknife CV)
---
Training datasets |  Model used |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  Gaussian NB |  87.07 |  89.70 |  88.38 |  0.77 |  0.88
|  Decision Trees |  81.21 |  78.59 |  79.90 |  0.60 |  0.80
|  Random Forest |  89.90 |  91.11 |  90.51 |  0.81 |  0.91
|  XGBoost |  91.52 |  91.31 |  91.41 |  0.83 |  0.91
|  PSe-MA (UK) |  90.04±0.05 |  91.14±0.06 |  90.60±0.002 |  0.84±0.09 |  0.90±0.08
S628 |  Gaussian NB |  93.29 |  96.83 |  95.06 |  0.90 |  0.95
|  Decision Trees |  83.71 |  91.75 |  87.74 |  0.76 |  0.88
|  Random Forest |  97.76 |  98.10 |  97.93 |  0.96 |  0.98
|  XGBoost |  97.12 |  98.41 |  97.77 |  0.96 |  0.98
|  PSe-MA (UK) |  98.49±0.02 |  98.49±0.01 |  98.41±0.08 |  0.97±0.006 |  0.98±0.09
M994 |  Gaussian NB |  90.25 |  87.71 |  88.98 |  0.78 |  0.89
|  Decision Trees |  84.32 |  83.90 |  84.11 |  0.68 |  0.84
|  Random Forest |  91.31 |  89.62 |  90.47 |  0.81 |  0.90
|  XGBoost |  91.74 |  91.53 |  91.63 |  0.83 |  0.92
|  PSe-MA (UK) |  95.40±0.08 |  95.40±0.01 |  94.73±0.05 |  0.89±0.04 |  0.94±0.06

Table 2: Different ML models (Jackknife CV) compared with UK on our new set of
features. The performance of PSe-MA is at par with XGBoost for H990 data,
however, it outperformed the other models for the remaining two data sets with
a Bonferroni Comparison (BC) value of 3.

##  7 Conclusion

According to the central dogma of molecular biology, RNA is the bridging
molecule between the information storage molecule, DNA, and the information
carrier molecule, protein. Besides the canonical A,G, C, and U bases, RNA
contains approximately 120 modified bases and sugars. These modified bases and
sugars play an essential role in the structural diversity and function of RNA.
The most abundant modification found in RNA is pseudouridine, an isomerized
form of uridine. Owing to the prohibitive costs and time associated with
determining the $\psi$ sites in an RNA experimentally, computational
prediction methods are often used. In this study, we present ’Pse-MA’, a data-
driven, utility kernel-based SVM model to predict the $\psi$ sites given the
sequence information alone. PSe-MA has shown a significant increase in
prediction accuracy (0.95, on average, compared to 0.72 of the state-of-the-
art models). When validated using two unseen datasets, Pse-MA has achieved an
accuracy of 97.54% (average). Apart from being the best-performing prediction
model among the set of existing baselines and accepted benchmark methods, our
model, Pse-MA (SVM Utility Kernel) is able to generalize remarkably well on
unseen test/validation data. Based on the current results, we are quite
encouraged to apply this methodology to develop prediction methods for the
other important functional modifications in RNA such as methylated Adenines
and Cytidines. It would be worthwhile to explore if Deep learning-based
feature extraction helps in further improvement of the prediction performance
(preferably very close to $100\%$) given we are able to generate a
sufficiently large corpus.

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## Appendix

##  Appendix A Results: PSe-MA compared with PseUI and iRNA-PseU model; 5-fold
cross validation

In K-fold CV, the data is divided into K-folds. The $k-1$ folds are used for
training and the $k^{th}$ fold is tested, and the process is repeated $k$
times, each time with a different subset for train and test (refer tables 3
and 4 ).

SVM Utility kernel against PseUI and iRNA-PseU models; with 5-fold CV
---
Training datasets |  Model used |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  iRNA-PseU (rbf) |  63.21 |  62.34 |  61.32 |  0.43 |  0.65
|  iRNA-PseU (linear) |  65.32 |  64.32 |  63.89 |  0.41 |  0.58
|  iRNA-PseU (UK) |  66.21±0.001 |  59.98±0.02 |  61.92±0.07 |  0.34±0.008 |  0.55±0.01
|  PseUI (rbf) |  64.82 |  63.25 |  64.87 |  0.56 |  0.68
|  PseUI (linear) |  65.78 |  64.65 |  66.66 |  0.47 |  0.74
|  PseUI (UK) |  70.76±0.09 |  69.54±0.07 |  71.33±0.08 |  0.46±0.05 |  0.50±0.04
|  PSe-MA (rbf) |  70.30 |  81.62 |  75.96 |  0.52 |  0.76
|  PSe-MA (linear) |  63.03 |  76.97 |  70.00 |  0.41 |  0.70
|  PSe-MA (UK) |  89.52±0.01 |  89.52±0.031 |  89.49±0.02 |  0.78±0.06 |  0.89±0.071
S628 |  iRNA-PseU (rbf) |  64.65 |  64.33 |  64.49 |  0.29 |  0.81
|  iRNA-PseU (linear) |  67.43 |  67.83 |  67.77 |  0.43 |  0.69
|  iRNA-PseU (UK) |  68.55±0.06 |  69.33±0.09 |  68.61±0.04 |  0.51±0.05 |  0.69±0.02
|  PseUI (rbf) |  62.10 |  71.02 |  66.56 |  0.33 |  0.69
|  PseUI (linear) |  64.32 |  71.90 |  65.65 |  0.34 |  0.61
|  PseUI (UK) |  67.33±0.04 |  68.79±0.01 |  72.73±0.05 |  0.33±0.06 |  0.69±0.02
|  PSe-MA (rbf) |  90.10 |  94.92 |  92.51 |  0.85 |  0.93
|  PSe-MA (linear) |  69.01 |  93.02 |  81.05 |  0.81 |  0.64
|  PSe-MA (UK) |  97.69±0.07 |  97.69±0.04 |  97.61±0.01 |  0.95±0.02 |  0.97±0.05
M994 |  iRNA-PseU (rbf) |  72.32 |  61.32 |  65.4 |  0.32 |  0.75
|  iRNA-PseU (linear) |  73.31 |  61.83 |  63.07 |  0.48 |  0.65
|  iRNA-PseU (UK) |  79.87±0.05 |  60.81±0.01 |  70.34±0.07 |  0.41±0.008 |  0.75±0.06
|  PseUI (rbf) |  73.67 |  64.33 |  70.14 |  0.53 |  0.67
|  PseUI (linear) |  74.58 |  66.31 |  70.44 |  0.41 |  0.77
|  PseUI (UK) |  75.43±0.08 |  67.73±0.03 |  71.32±0.06 |  0.39±0.02 |  0.79±0.01
|  PSe-MA (rbf) |  78.62 |  77.34 |  77.97 |  0.56 |  0.78
|  PSe-MA (linear) |  75.44 |  74.80 |  77.92 |  0.56 |  0.78
|  PSe-MA (UK) |  91.45±0.007 |  91.45±0.01 |  91.42±0.09 |  0.83±0.04 |  0.91±0.02

Table 3: 5 fold Cross-validation Results-iRNA-PseU and PseUI used RBF SVM on
their data; our method PSe-MA used Utility Kernel on new biological features
extracted in this work; the three feature vectors are made to run on three SVM
kernels viz. RBF, linear and utility kernel. Utility Kernel outperformed the
other methods with a Bonferroni Comparison (BC) value of 3 on every dataset.

Different models (ML) on the three training datasets using PSe-MA
---
Training datasets |  Model used |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  GausianNB |  88.41 |  88.41 |  88.48 |  0.77 |  0.88
|  Decision Trees |  74.07 |  74.07 |  74.24 |  0.48 |  0.74
|  Random Forest |  75.97 |  75.97 |  75.96 |  0.52 |  0.75
|  XGBoost |  89.48 |  89.48 |  89.49 |  0.78 |  0.89
|  PSe-MA (UK) |  89.52±0.001 |  89.52±0.004 |  89.49±0.02 |  0.78±0.03 |  0.89±0.07
S628 |  GausianNB |  94.78 |  94.78 |  94.75 |  0.89 |  0.94
|  Decision Trees |  85.59 |  85.59 |  85.51 |  0.71 |  0.85
|  Random Forest |  83.1 |  83.1 |  83.13 |  0.66 |  0.83
|  XGBoost |  97.04 |  97.04 |  96.98 |  0.93 |  0.97
|  PSe-MA (UK) |  97.69±0.03 |  97.69±0.04 |  97.61±0.09 |  0.95±0.02 |  0.97±0.07
M994 |  GausianNB |  88.93 |  88.93 |  88.88 |  0.77 |  0.88
|  Decision Trees |  80.66 |  80.66 |  80.62 |  0.61 |  0.8
|  Random Forest |  77.84 |  77.84 |  77.75 |  0.55 |  0.77
|  XGBoost |  90.88 |  90.88 |  90.00 |  0.81 |  0.9
|  PSe-MA (UK) |  91.45±0.01 |  91.45±0.03 |  91.42±0.01 |  0.83±0.10 |  0.91±0.08

Table 4: Different ML models (5-fold CV) compared with our new set of
features. Utility Kernel outperformed the other methods with a Bonferroni
Comparison (BC) value of 3 on every dataset.

##  Appendix B Results: PSe-MA compared with PseUI and iRNA-PseU models;
66-33% split

The 66%-33% train-test split is the standard way of CV where 66% of data is
used for training and 33% of data is used for reporting the performance of the
model (refer tables 5 and 6).

PSe-MA compared with PseUI and iRNA-PseU models; 66-33% split
---
Training datasets |  Training datasets |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  iRNA-PseU (rbf) |  62.41 |  60.23 |  62.44 |  0.32 |  0.56
|  iRNA-PseU (linear) |  60.32 |  61.24 |  63.43 |  0.31 |  0.58
|  iRNA-PseU (UK) |  62.34±0.03 |  58.65±0.02 |  63.22±0.07 |  0.27±0.05 |  0.59±0.06
|  PseUI (rbf) |  63.45 |  65.64 |  68.91 |  0.38 |  0.64
|  PseUI (linear) |  68.93 |  66.80 |  65.43 |  0.32 |  0.52
|  PseUI (UK) |  71.11±0.09 |  68.34±0.03 |  70.32±0.002 |  0.44±0.04 |  0.61±0.01
|  PSe-MA (rbf) |  79.81 |  76.21 |  77.32 |  0.42 |  0.71
|  PSe-MA (linear) |  77.78 |  80.61 |  79.20 |  0.79 |  0.58
|  PSe-MA (UK) |  90.18±0.03 |  90.18±0.01 |  90.2±0.09 |  0.8±0.04 |  0.9±0.009
S628 |  iRNA-PseU (rbf) |  65.45 |  63.76 |  65.76 |  0.38 |  0.73
|  iRNA-PseU (linear) |  62.45 |  64.44 |  62.32 |  0.31 |  0.77
|  iRNA-PseU (UK) |  68.55±0.07 |  69.33±0.01 |  68.61±0.06 |  0.51±0.08 |  0.69±0.02
|  PseUI (rbf) |  64.32 |  75.02 |  68.62 |  0.54 |  0.54
|  PseUI (linear) |  64.32 |  72.31 |  67.43 |  0.23 |  0.64
|  PseUI (UK) |  67.33±0.06 |  68.79±0.03 |  72.73±0.01 |  0.33±0.05 |  0.69±0.02
|  PSe-MA (rbf) |  79.99 |  76.54 |  75.45 |  0.77 |  0.83
|  PSe-MA (linear) |  88.39 |  96.88 |  92.31 |  0.93 |  0.85
|  PSe-MA (UK) |  94.18±0.08 |  94.16±0.01 |  94.17±0.07 |  0.88±0.04 |  0.94±0.001
M994 |  iRNA-PseU (rbf) |  72.21 |  65.23 |  68.32 |  0.42 |  0.64
|  iRNA-PseU (linear) |  72.45 |  66.54 |  69.82 |  0.41 |  0.76
|  iRNA-PseU (UK) |  79.87±0.08 |  60.81±0.04 |  70.34±0.06 |  0.41±0.09 |  0.75±0.007
|  PseUI (rbf) |  74.21 |  65.51 |  71.23 |  0.38 |  0.67
|  PseUI (linear) |  73.56 |  67.83 |  71.21 |  0.45 |  0.76
|  PseUI (UK) |  76.58±0.01 |  69.83±0.02 |  71.32±0.04 |  0.52±0.07 |  0.65±0.05
|  PSe-MA (rbf) |  78.82 |  79.32 |  75.43 |  0.61 |  0.61
|  PSe-MA (linear) |  77.50 |  80.92 |  79.17 |  0.79 |  0.58
|  PSe-MA (UK) |  91.0±0.07 |  91.0±0.009 |  91.0±0.01 |  82.0±0.05 |  91.0±0.09

Table 5:  66-33% Cross-validation Results:iRNA-PseU and PseUI used RBF SVM on
their data; our method PSe-MA used Utility Kernel on new biological features
extracted in this work; the three feature vectors are made to run on three SVM
kernels viz. RBF, linear, and utility kernel. Utility Kernel outperformed the
other methods with a Bonferroni Comparison (BC) value of 3 on every dataset.

Different ML models on three training datasets (66-33 % CV) using PSe-MA
---
Training datasets |  Training datasets |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H990 |  GausianNB |  88.9 |  88.9 |  88.1 |  0.77 |  0.88
|  Decision Trees |  77.95 |  77.95 |  77.98 |  0.55 |  0.77
|  Random Forest |  78.56 |  78.56 |  78.59 |  0.57 |  0.78
|  XGBoost |  90.1 |  90.1 |  90.18 |  0.8 |  0.89
|  PSe-MA (UK) |  90.18±0.04 |  90.18±0.03 |  90.2±0.009 |  0.8±0.06 |  0.9±0.01
S628 |  GausianNB |  91.44 |  91.44 |  91.34 |  0.82 |  0.91
|  Decision Trees |  80.57 |  80.57 |  80.28 |  0.61 |  0.8
|  Random Forest |  84.6 |  84.6 |  84.61 |  0.69 |  0.84
|  XGBoost |  93.83 |  93.83 |  93.75 |  0.87 |  0.93
|  PSe-MA (UK) |  94.18±0.02 |  94.16±0.04 |  94.17±0.07 |  0.88±0.09 |  0.94±0.08
M994 |  GausianNB |  89.1 |  89.1 |  89.1 |  0.78 |  0.89
|  Decision Trees |  81.71 |  81.71 |  81.41 |  0.63 |  0.81
|  Random Forest |  81.59 |  81.59 |  81.73 |  0.63 |  0.81
|  XGBoost |  89.51 |  89.51 |  89.42 |  0.78 |  0.89
|  PSe-MA (UK) |  91.0±0.009 |  91.0±0.008 |  91.0±0.001 |  82.0±0.004 |  91.0±0.006

Table 6: Different ML models (66-33% CV) compared with our new set of
features. Utility Kernel outperformed the other methods with a Bonferroni
Comparison (BC) value of 3 on every dataset.

##  Appendix C Results on additional data

In addition to the training datasets, Chen et al.provided two independent
testing datasets for H. sapiens and S. cerevisiae, namely H200 and S200, but
not for M. musculus. The results are in the table 7

5 fold CV with different ML models on testing datasets
---
Testing datasets |  Model used |  Sensitivity |  Specificity |  Accuracy |  MCC |  AUC
H200 |  Decision tress |  77.82 |  78.92 |  77.79 |  0.74 |  0.84
|  Random forrest |  90.25 |  91.44 |  92.85 |  0.85 |  0.97
|  XGBoost |  91.72 |  90.25 |  93.28 |  0.87 |  0.82
|  SVM rbf |  74.75 |  77.14 |  75.97 |  0.85 |  0.67
|  SVM linear |  74.62 |  76.92 |  75.79 |  0.53 |  0.84
|  SVM Utility |  95.38±0.02 |  95.38±0.005 |  95.40±0.033 |  0.90±0.009 |  0.95±0.01
S200 |  Decision tress |  85.24 |  86.75 |  86.00 |  0.86 |  0.72
|  Random forrest |  99.04 |  99.04 |  99.04 |  0.97 |  0.98
|  XGBoost |  98.03 |  98.55 |  98.43 |  0.99 |  0.97
|  SVM rbf |  96.65 |  96.14 |  96.38 |  0.99 |  0.93
|  SVM linear |  89.61 |  89.64 |  89.63 |  0.96 |  0.79
|  SVM Utility |  99.69±0.07 |  99.69±0.002 |  99.68±0.009 |  0.99±0.02 |  0.99±0.06

Table 7: 5 fold Cross-validation Results with a comparison of different ML
models on two of the testing datasets

##  Appendix D The sequence information of three Datasets- H.sapiens,
S.cerevisiae, and M.musculus M.

This study used three benchmark datasets for training: H990, S628, and M944.
These are the same datasets used by iRNA-PseU and PseUI methods. These
datasets are curated from the experimentally found $\psi$ sites from RMBase
for H. sapiens, M. musculus, and S. cerevisiae. The negative dataset is made
of RNA sequences that were experimentally confirmed to not have $\psi$ sites.
In addition to the training datasets, Chen et al. [4] provided two independent
testing datasets for H. sapiens and S. cerevisiae, namely H200 and S200, but
not for M. musculus.

Species |  Name of the training dataset |  Length of the RNA sequence |  Number of positive samples |  Number of negative samples
---|---|---|---|---
H.sapiens |  H-990 |  21 |  495 |  495
S.cerevisiae |  S-628 |  31 |  314 |  314
M.musculus |  M-994 |  21 |  472 |  472

Table 8: The sequence information of the three datasets

Species |  Name of the training dataset |  Length of the RNA sequence |  Number of positive samples |  Number of negative samples
---|---|---|---|---
H.sapiens |  H-200 |  21 |  100 |  200
S.cerevisiae |  S-200 |  31 |  100 |  200

Table 9: Additional Data - The sequence information of the two testing
datasets