Principle Components Analysis based frameworks for efficient missing data imputation algorithms
Authors: Thu Nguyen
Hoang Thien Ly
Michael Alexander Riegler
Pål Halvorsen
Venue: NeurIPS 2022 Submitted (2022)

Abstract: Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation techniques. Meanwhile, the data nowadays tends toward high-dimensional.   
Therefore, in this work, we propose \textit{Principal Component Analysis Imputation} (PCAI), a simple but versatile framework based on Principal Component Analysis (PCA) to speed up the imputation process and alleviate memory issues of many available imputation techniques, without sacrificing the imputation quality in term of MSE. In addition, the frameworks can be used even when some or all of the missing features are categorical, or when the number of missing features is large.
Next, we introduce  \textit{PCA Imputation - Classification} (PIC), an application of PCAI for classification problems with some adjustments.
We validate our approach by experiments on various scenarios, which shows that PCAI and PIC can work with various imputation algorithms, including the state-of-the-art ones, and improve the imputation speed significantly while achieving competitive mean square error/classification accuracy compared to direct imputation (i.e., impute directly on the missing data).



Principal Components Analysis based frameworks for efficient missing data imputation algorithms
Anonymous Author(s)
Affiliation
Address email
Abstract
Missing data is a commonly occurring problem in practice. Many imputation meth- ods have been developed to fill in the missing entries. However, all of them can scale to high-dimensional data, especially the multiple imputation techniques. Meanwhile, the data nowadays tending toward nigh-dimensional. Therefore, in this work, we propose Principal Component Analysis Imputation (PCAI), a simple but versatile framework based on Principal Component Analysis (PCA) to speed up the imputation process and alleviate memory issue of many available imputation techniques, without sacrificing the imputation quality in term of MSE. In addition, the frameworks can be used even when some or all of the missing features are categorical, or when the number of missing features large. Next, we introduce PCA Imputation Classification (PIC), an application of PCAI for classification problem with some adjustment. We validate our approach by experiments on vari- ous scenarios, which shows that PCAI and PIC can work with various imputation algorithms, including the state-of-the-an ones and improve the imputation speed significantly, while achieving competitive mean square error/classificatin accuracy compared to direct imputation (i.e., impute directly on the missing data).
10
11
12
14
16
Introduction
17
Despite recent efforts in directly handling missing data 2 4), missing data imputation approaches [5] 7 remain commonly used. This is because directly handling missing data can be complicated and usually are developed for specific target problems or models, while imputation can be more versatile. Specifically, important advantage of imputation is that the imputed data becomes complete, i.e., no longer have any missing values. Therefore, it is easier to continue with other preprocessing steps, analysis, and data visualizations. Furthermore, and choose the best one by using the available packages or software tools for non-missing data. Meanwhile, directly handling missing data strategies do not have these advantages. They are more complicated and not that readily available.
18
20
22
can deploy many models
24
25
26
Many techniques have been developed for missing data imputation, ranging from traditional tech- niques such as MICE (5). K-Nearest Neighbors to recent machine lcarning/decp learning techniques such as GAIN (6) DL-GSA [7]. However, most of them are computationally expensive for big datasets. For example, experiments in g show that under their experiment settings, for Fashion MNIST M dataset of 70,000 samples and 784 features, the MICE [5] and missForest [10] tech- niques are unable to finish the imputation process within three hours for a missing rate (the ratio between the number of missing entries versus the total number entries in the dataset) of 20%. Since
28
30
32
33
34
datasets nowadays are trending towards larger sizes I1. with hundreds of thousands of features
35
12
it is crucial to speed up the available imputation techniques. Taking into account resource
Submitted to 36th Conference on Neural Information Processing Systems (NeurIPS 2022). Do not distribute.

---

36
consumption and availability such speed up cannot be achieved by only providing more and better
37
hardware but by the development of new methods.
38
To achieve this goal, this work introduces two novel frameworks based on Principal Component Analysis (PCA) to speed up the imputation process of many available techniques or the imputation- classification process for missing data classification problems, The first framework, PCA Imputation (PCAI) is proposed to speed up the imputation speed by partitioning the data into the fully observed features partition and the partition of features with missing data. After that, the imputation of the missing part is performed based on the union of the PCA- reduced version of the fully observed part and the missing part. Interestingly, it turns out that the method has a great potential to aid the performance of methods that rely on many parameters, such as Deep Learning imputation techniques. Mcanwhile, the second one, PCA Imputation Classification (PIC) is proposed to deal with the missing data classification problems where dimension reduction is desirable in advance of the model training step. PIC is based on PCAI with some modifications. Note that these frameworks are different from the methods developed for principal component analysis under missing data presented in 1 which are about how to conduct PCA when the data contains missing values.
39
40
41
42
43
44
45
48
47
48
49
51 In summary, the contributions of this article are: (i) we introduce PCAI to improve the imputation
52 speed of many available imputation techniques; (ii) we introduce PIC to deal with missing data
53 classification problems where dimension reduction desirable; (iii) we analyze the potential strength and drawbacks of these approaches; and (iv) we illustrate via experiments that our frameworks can work with various imputation strategies while achieve comparable or even lower mean square error/higher classification accuracies compared to the corresponding original approaches, and alleviate the memory issue in some approaches.
54
55
56
57
The rest of the paper is organized as follows. In Section 2 and Section 3 we review some related work in the field of missing data, and review two popular formulations of PCA. Next, in Section Section 5 and Section 6 we introduce our novel PCAI and PIC frameworks, and study their we demonstrate their capabilities via experiments on various datasets. The paper ends with conclusions, remarks, and future works in
58
59
60
61
relation previous works, respectively. After that, in Section 7
62
63
Section g
2
Related Works
65
Various works have been published on missing data imputation to deal with different data analysis situations. As example, if one is interested in modeling the uncertainty associated with the imputation, suitable approaches can be multiple or Bayesian imputation techniques such as multiple imputations using Deep Denoising Autoencoders (15). Bayesian Principal Component Analysis- based imputation [66], and extreme learning machine multiple imputation [7]. In addition, graphical models can be prominent candidates when transparency, estimability, and testability are desirable, and these approaches can provide meaningful performance guarantees even if the missing values are not at random [88. Next, for continuous data, matrix completion techniques such as Fast Alternating Least Squares 19.. softImpute (20) can quickly give good results. In biology, the missing values are often categorical, and the imputed values need to be interpretable. In such cases, classification techniques or tree-based methods such as decision trees and fuzzy clustering with iterative learning (DIFC) (1]. missForest [00. the DMI algorithm [22]. and sequential regression trees (3) are well-suited. In addition, some recently developed methods that can handle mixed missing data are SICE [24], FEMI 25), and HCMM-L.D (26). When the sample sizes are large enough compared to the number of features, deep learning techniques such as Multiple Imputation Using Deep Denoising Autoencoders
67
68
69
70
71
72
73
74
75
76
78
79
80
[5], DL-GSA 17). and Swarm Daelligence-Decy Neural Network (27] can be powerful imputers. However, it is worth noting that deep learning methods usually require more data than statistical imputation approaches. Some other popularly used missing data imputation methods are multiple imputation by chained equation (MICE) [5], K-nearest Neighbors imputation (KNNI) 28] and mean
81
82
83
84
imputation 28
85 In addition, for the purpose of data imputation and data type. for classification, the impact of
86 imputation techniques on different classifiers may vary. Specifically, (28) compares the performance
87 of logistic regression with regularization, k-nearest neighbours (kNN), random forest, classification
88 tree, and xghoost classifiers (28) on datasets with missing entries. They use different imputation
89 methods (mean imputation/ MICE imputation [5) missForest [00] random imputation/ softlmpute
2

---

90
20V hot deck imputation, KNN imputation) and compare the performance. According to the paper, with regularization
91
mean imputation seems to outperform other counterparts for logistic regression and KNN, random imputation wins for random forest, missForest seems to be the best imputer for classification tree, and hot deck imputation the best for xghoost.
93
94
With the rapid growth of data size M [2]. it is necessary to speed up the available imputation methods because many current approaches remain too slow for big datasets, pointed out in an example in Section [1] This is where a popular dimension reduction method like PCA can come to use. PCA projects the original nigher-dimensional dataset into a representation of lower dimensionality by extracting and retaining important information from the data and expressing this new information based on set of orthogonal vectors known as principal components. Its goal is to find linear transformations of the original data that retain the maximal amount of variance. Note that there are some works on PCA under data missingness. For example, [[3] considers the problem of finding principal components as an optimization problem of an objective function and proposes iterative 29 proposes a multiple imputation method for the estimates of the parameters (components and axes) of PCA to take into account the variability due to missing values.
95
96
97
98
99
100
101
102
103
solutions to it. On the other hand,
105
However, our work is different from these works in the sense that they target the problem how to perform PCA for a dataset with missing data. Meanwhile, our frameworks utilize PCA to speed up the imputation processor to reduce the ratio between the number of features and the sample size.
107
3 Preliminaries
108
Let X = [may] where i m;j I..... be input data matrix of n samples, p features. In addition, assume that the features are centered and scaled. We review two popular formulations of PCA, which we refer as PCA formulation 1 (PCA-form1) and PCA formulation 2 (PCA-form2).
110
111
112
3.1
PCA based covariance matrix (PCA-forml)
Let Σ be the covariance matrix of X. Next, let (Λ1, vi). (Aps Vp) be the sorted eigenvalue- eigenvector pairs of Σ such that \ 2 x2 2 ... 2 Ap 2 0. Suppose that we choose the first pairs 115 for dimension reduction. Then the amount of variance explained by these r pairs is
113
+ +
(1)
116
In addition, let V = [V1, V2,..., vyl. Then the dimension reduced version of X is XV.
117
3.2
PCA based on the input matrix X (PCA-form2)
118
The solution of PCA can also be produced based on the singular value decomposition of X 330
X = UDWT
119
where U is an n X p orthogonal matrix, W is a x orthogonal matrix, and D is a X diagonal matrix whose diagonal elements are di 2 d2 2 2 dp 0. Suppose that eigenvalues are used,
120
then the projection matrix is V W, W where W, consists of the first columns of Then
121
122
the dimension reduced version of X is also XV.
123
4
PCA Imputation (PCAT)
124
In this section, we detail our PCAI framework, PCA based framework that capable of significantly improving the imputation speed of an imputer for high dimensional data, alleviating the memory issue for many approaches.
125
126
127 To start with some notations, let pea(A) be a function of a data matrix A. The function returns AA V) where RA is the PCA-reduced version of A, and V is the projection matrix where the 7th column of V is the eigenvector corresponding to the 7th largest eigenvalue. In addition, denote by
128
129
AUE B the columnwise concatenation of two data partition A and B of relevant sizes. Next, suppose
131
that we have dataset D FUM, where J consists of data from fully observed features and M
consists of data from features with missing values.
3

---

133
The framework is as depicted in Algorithm 1 We first conduct dimension reduction on the fully observed partition F, which produces a reduced version R of F. Then, the imputation of M is done on the set R. U M instead of 'D F U M as how imputations are usually done (i.e., impute directly on the original missing data). In conducting dimension reduction, we expect to reduce the dimension
134
135
136
137
of the fully observed partition so that the imputation of M can be faster.
Algorithm 1 PCAI framework
Require:
= FFUM M where F is the fully observed partition and M is the partition with missing values
Imputer /
PCA algorithm pea
Procedure:
(). +pcaFF)
M¹ f- the imputed version of M based on R UUM M
return Imputed version M' of M
138
For the choice of the PCA formulation, note that if the number of samples is larger than the number of features in F, then the size of the covariance matrix smaller than the size of F. Therefore, one may expect using the formulation of PCA based on the covariance matrix, as in Section 3.1 to be faster. Meanwhile, if the number of features in F is larger than the sample size, then the covariance matrix of F is larger than F. Therefore, in such a case, it is better to use the PCA formulation based on the data itself, i.e. formulation as in Section 3.2
139
140
141
142
143
144
One may reckon that using R U M instead of F U M may lead to loss of information due to dimension reduction and therefore lower the quality of imputation. However, as will be illustrated in the experiments, the differences between the mean squared error of the imputed version versus the ground truth for these approaches are only slightly different, and many times, PCAI seems to be slightly better. This is possibly because PCA retains the important information from the data while removing some noise, and therefore helps improving the imputation quality. However, PCAI also has some shortcomings. For problems where the sample size n is smaller than the number of features in the fully observed block q. PCA-forml is used, the covariance matrix has the size of q X q. which is bigger than the size q of the fully observed partition F. This may make the PCA dimension reduction process become computationally expensive, rendering PCAI to be slower than imputing directly on the original missing data. This issue will be illustrated in the experiment section.
145
146
147
148
149
151
153
154
PCAI for classification (PIC)
155
158
In this section, discuss straightforward application of PCAI in classification, with slight modification for classification problems where it is desirable to conduct a dimension reduction before training a model, such as when the number of features is much larger than the sample size.
157
159
Since PCAI conducts PCA on the fully observed partition F, it reduces the dimensions for portion of the data. Therefore, rather than imputing values using the PCAI framework and then conducting a dimension reduction step on F M', one can perform dimension reduction on M' to get R', a PCA-reduced version of M'. Then, one can use FU' as reduced dimension data. As will be shown the experiments, this speeds up the imputation and classification process significantly. This is the basic idea of our Principle component Imputation for Classification (PIC) framework.
160
161
162
163
164
165
PIC operates as shown in Algorithm 2 The procedure starts by performing PCA on the training fully observed partition Ferain. which gives the reduced version Rerain of Ftrain and a projection matrix V. Next, we project Fiest on V to get the reduced version Reest of Frest- Then, we impute Merain on Rirain U to get the imputed version M'rrinn Next, we impute Meest on Reest U Meest set to true, we perform dimension Then, we train the classifier on Rerain U R'yains i.e., the union of the reduced version of Ftrain and the reduced version of Mtrain- For prediction of a vector x E D, (xF, XM). After that, we can project X, on V to get a projection r. Similarly, we can project XM on V to a get projection r'. Finally, we can predict the label of x using
186
167
168
to get the imputed version My After that, if reducemiiss
169
170
reduction on
171
172
we can decompose x into
173
the classifier C' with input (r, r').

---

175
Note that reducemiss is an option. When the number of features in the missing partition M is large, one may be interested in reducing the dimension of M', and therefore, set reducemiss to True. However, when the number of features in the missing partition is small, one may want to keep it to False. Also, since PIC is straightforward application of PCAI for classification, the choice of PCA formulation should be used is similar to PCAI, which is analyzed in the previous section.
178
177
178
179
Algorithm 2 PIC framework
Require:
D FU M where F is the fully observed partition and .M is the partition with missing values reduucemis = True/ / F False: if True, perform dimension reduction on the imputed partitions;
False, do not perform dimension reduction on the imputed partitions
-Ftrain Freat: the training and testing data of the fully observed partition F, respectively
-Mrrain Mtest the training and testing data of the partition that has missing data M, respectively
Imputer I, classifier C, PCA algorithm pea.
Procedure:
(Rrrains V) c pcppaaaaaaaa
Riest t- Frast V
M Mirain -imputed version of Merain based Revain U Marain
Miest + -imputed version of MMest based on Reest U Maest if reducemiss then
(Rerain: W) 4- pca(M
Rlest MMees
Train the classifier C' based on Rerain U Ri
Classify based on Reest Ryysst
else
Train the classifier based on Rivain UM
Classify based on Reest U Mleat
end
return trained classifier C
6 Relation to previous works
181
Various works have been done on PCA that are related to missing data, which mostly can be categorized into missing values imputation using PCA, or dimension reduction using PCA under missing values. Some typical works that make use of PCA for missing values imputation are probabilistic PCA for missing flow volume data imputation [T: chunk-wise iterative PCA for data imputation datasets with many samples 33]; 14 missing data that help in case of sparse, high dimensional data; [33] analyze maximum likelihood PCA (MLPCA) maximum likelihood missing data imputation; and 34] proposed an imputation approach based on PCA and factorial analysis for mixed data.
182
184
proposes fast algorithm for PCA under
186
188
189
Next, PCA under missing values was first studied in [3), where only one component and one imputation iteration are used. After that, (36) proposes method based on MLPCA, where the method assigns large variance to missing values prior to implementing the method, which aim to guide the algorithm to fit PCA model disregarding those points. Also, [37] introduce EM algorithm for building PCA model that can deal with missing data. More recently, [8 proposes new techniques for building a PCA model with missing data: known data regression (KDR), projection to the model plane, KDR with principal component regression.In addition, [39 studies estimation and imputation in Probabilistic PCA when the data is missing not at random.
190
192
194
196
197
Different from the previous approaches, PCAI is framework to speed up the imputation process, which can be used with various imputation methods, including the aforementioned PCA imputation algorithms and the state-of-the-an imputation algorithms such as softlmpute [20]. MissForest [10),
196
199
200
GAIN ()). addition, note that since PCAT and PIC conduct dimension reduction on the fully
observed partition F, and not the missing portion M if reduce = False, they can handle missing
202
data even categorical features presents in the missing portion M, when being used with imputers
that's capable of handling categorical/mixed data (MissForest [00] SICE [4]. FEMI (25) etc.). In
5

---

Table 1: Description of datasets used in our experiments
Dataset
# Classes
# Features
# Samples
Parkinson 42
2
754
756
Fashion MNIST
10
784
70000
Gene 43
5
20531
801
204
addition, even if there exists categorical and continuous features in M; or reducemiss True and
205
there exists categorical and continuous features M, one can easily adjust the algorithm to conduct PCA on continuous features only. The previously mentioned PCA based approaches are, however, can only be used for continuous data, because PCA requires the data to be continuous.
207
208
7
Experiments
209
7.1
General experiment settings
We compare the speed (seconds) and MSE of PCAI with direct imputation (DI), i.e., use imputation algorithm directly on the dataset. The imputation approaches used for comparison: softImpute 20 40) MissForest [10] and Multiple Imputation by Chained Equation (MICE) [1,44,
211
213
KNN Imputation (KNNI), GAIN 6 are implemented with default configurations. The codes will be available upon the acceptance of the paper. For PIC, we compare the five fold cross-validation (CV) score (aceuracy, speed) of PIC when dimension reduction is applied on the imputed missing part (PIC-reduce), when dimension reduction is applied on the imputed missing part (PIC), and when PCA is applied to the imputed version on the full missing data (DI-reduce), and when no dimension reduction applied to imputed data after direct imputation (DI). Here, the default PCA formulation is PCA-forml, unless specified otherwise. For all PCA computation, the number of cigenvectors is chosen that the minimum amount variance explained 95%.
215
217
218
219
220
221
Details of the datasets used in the experiments are available in Table I All experiments are run on an AMD Ryzen 7 3700X CPU with 8 Cores, 16 processing threads, 3.6GHz, and 16GB RAM.W. terminate an experiment if no result is produced after 6,500 seconds of running or there arises memory allocating issue, and we denote this NA in the result tables.
223
224
225
7.2
Performance of PCAI and PIC when the missing values in M are randomly simulated
Table 2: (MSE, speed) for PCAI and direct imputation (DI) on the Parkinson dataset with = 700.
missing rate
Imputer
Strategy
20%
40%
60%
PCAI
(0.073, 0.860)
(0.185, 0.774) (0.188, 4.043)
(0.305, 0.875)
softImpute
DI
(0.072, 4.097)
(0.308, 4.467)
PCAI
(0.091, 139.811) NA
(0.186, 85.241) NA
(0.369, 109.815) NA
MICE
DI
PCAI
(0.254, 45.046) (0.608, 69.839)
(0.538, 43.938)
(0.779, 43.956
GAIN
DI
(1.097, 70.548)
(1.369, 70.293)
PCAI
(0.064, 188.324) (0.058, 905.002)
(0.163, 178.849)
(0.292, 138.085)
missForest
DI
(0.160, 692.150)
(0.258, 449.415)
PCAI
12., 0.355) (0.113, 0.310)
(0.299, 0.398)
(0.466, 0.416) (0.426, 0.372)
KNNI
DI
(0.274, 0.337)
228
Note that any datasets can be rearranged so that the first g features are not missing and the remaining ones are missing. Therefore, without loss of generality, we assume that the first q features of each
227

---

Table 3: (MSE, speed) for PCAI and DI on the Fashion MNIST dataset with q = 700. MissForest results all are NA, and therefore are removed from the tables.
missing rate
Imputer
Strategy
20%
40%
60%
PCAI
(0.032, 22.408)
(0.066, 22.797)
(0.109, 25.603)
softImpute
DI
(0.032, 67.627)
(0.064, 69.349)
(0.107, 77.233)
PCAI
(0.027, 221...21886 NA
(0.055, 1374.558) NA
(0.095, 1641.962) NA
MICE
DI
PCAI
(0.053, 65.730) (0.041, 97.898)
(0.091, 68. (5.752)
(0.137, 69.743)
GAIN
DI
(0.079, 99.049)
(0.125, 96.317)
PCAI
(0.055, 1607.850) (0.049, 3042.752)
(0. 11,, 2033.153) (0.102 3659.300)
(0.180, 2272.370) (0.161, 3959.832)
KNNI
DI
dataset are missing, and the remaining ones contain missing value(s). Then, we simulated missing
229
data randomly on the missing partition M with missing rates 20%, 40%, and 60%. Here, missing
230
rate of 20% means that 20% of the entries in the missing partition M are missing. The results for Due to space limit, the results related to PIC on
such experiments are reported in Tables 2
Fashion MNIST are reported in the Appendix.
Table 4: Five fold CV results (accuracy, speed) of SVM Parkinson with g 700.
missing rate
Imputer
Strategy
20%
40%
60%
PIC-reduce
(0.862, 1.026)
(0.862, 1.137)
(0.862, 1.161)
softImpute
PIC
(0.858, 1 1.008)
(0.858, 1.079)
(0.859, 1.112)
DI-reduce
(0.861, 4.116)
(0.862, 4.424)
(0.861, 4.718)
DI
(0.858, 3.775)
(0.858, 3.912)
(0.855, 4.248)
PIC-reduce
(0.859, 204.605)
(0.861, 256.340)
(0.861, 2801,,40.2111 240.211)
MICE
PIC
(0.858, 524.739) NA
(0.859, 694.667) NA
(0.859, 925.426) NA
DI-reduce
NA
NA
NA
PIC-reduce
(0.857, 91.086)
(0.852, 102.861)
(0.848, 122.349)
GAIN
PIC
(0.851, 89.984)
(0.853, 104.773)
(0.853, 123.233)
DI-reduce
(0.855, 130.349)
(0.851, 149.864)
(0.851, 181.135)
DI
(0.846, 129.702)
(0.849, 152.031)
(0.852, 183.67)
PIC-reduce
(0.859, 204.850)
(0.861, 276.537)
(0.858, 153.783)
missForest
PIC
(0.858, 202.939)
(0.861, 277.067)
(0.858, 153.463)
DI-reduce
(0.861, 656.948
(0.862, 729 729)872)
(0.861, 472.230)
DI
(0.858, 655.750)
(0.861, 730.013)
(0.858, 472.388)
PIC-reduce
(0.858, 0.533)
(0.861, 0.462)
(0.862, 0.625)
KNNI
PIC
(0.858, 0.513)
(0.861, 0.462)
(0.862, 0.607)
DI-reduce
(0.862, 0.696)
(0.862, 0.642)
(0.859, 0.803)
(0.859, 0.438)
(0.859, 0.45)
(0.858, 0.552)
232
From the tables, it is clear that the proposed frameworks reduce the imputation time significantly while maintaining competitive MSFFclassification accuracy compared DI, in most of the cases. For example, at the missing rate 20% on the Parkinson dataset (Table 4.. when using GAIN for imputation, running time PIC-reduce(91. .086s) much lower compared to DI-reduce (130.349), the running time of PIC (1999884) is also much lower compared to DI (29.702). Another example can be seen from Table 2] for Parkinson dataset, at 20% missing rate, when PCAI applied to Forsst the running time reduces to 188.324s, which is almost 1/5 of the DI (905.002s). Next,
234
235
236
238

---

240
on Fashion MNIST (Table B), it is worth noticing that for MICE, DI cannot gives the results due to memory issue but PCAI can alleviate this issue and deliver the results.
241
242
For KNNI, the running time for KNNI between the PCAI approach and direct imputation for Parkinson ( is not much different. However, for the Fashion MNIST dataset, KNNI using the
244
PCAI framework obviously deliver competitive result in a significantly shorter time. Specifically,
245
KNNI a missing rate of 20% on Fashion MNIST gives result after only 1607. .800 seconds, while DI takes up to 5,002.752 seconds. This is because Fashion MNIST (70000 samples) has much more samples than Parkinson (756 samples), and KNN need do lot of pairwise comparison. Therefore,
246
247
248
PCAI and PIC would be extremely helpful for KNNI when the sample size and the number of fully observed features is large. Note that it does not require the number of features with missing data to
249
250
be large or small.
From Table 2 we can that PCAI generates lot of improvements in MSE for GAIN, in addition 252
to improvements in speed. This possibly because PCA reduces the number of features while the sample size remains the same, making such deep learning approach more applicable to the newly reduced data.
253
254
255
7.3
Performance on nonrandomly missing data
Therefore, we generate one-step monotone missing data on Fashion MNIST by first, randomly choose 20%, 40%, 60% of the samples. Then, make them become missing by deleting the lower right corner by deleting the intersection between the last rows and the last columns of each image array. The see that PIC-reduce is great improvement in speed compared to DI-reduce, and PIC is a significant improvement in speed compared to DI. This illustrates that PIC can work effectively even for con-randmmly missing data.
In many fields, the data are missing in monotone pattern rather than random 44
257
259
results reported in Table From the table,
261
Table 5: Five fold CV results (accuracy, speed) of SVM on monotone data generated on Fashion MNIST.
missing rate
Imputer
Strategy
20%
40%
60%
PIC-reduce
(0.889, 409.676)
(0.889, 421.671)
(0.889, 369.49)
softImpute
PIC
(0.889, 507.626
(0.89, 543.309)
(0.889, 480.452)
DI-reduce
(0.89, 439.268)
(0.89, 528.892)
(0.889, 395.646)
DI
(0.891, 738.494)
(0.891, 872.616)
(0.89, 646.781)
PIC-reduce
(0.886, 462.478)
(0.883, 429.173)
(0.882, 449.786)
GAIN
PIC
(0.886, 493.399)
(0.882, 484.232)
(0.881, 496.066)
DI-reduce
(0.891, 543.803)
(0.89, 431.947)
(0.89, 454.981)
DI
(0.892, 902.049)
(0.891, 754.794)
(0.891, 780.686)
7.4
PIC under different PCA formulations and number of missing features
264
The missing data in these experiments are generated at random as in Section 7.2 and the five fold cross validation results of SVM the Gene dataset with g = 15000, 20000, are shown in Table 6 and Table 7 From these tables, one can see clearly that for datasets where the number of features are significantly higher than the number of samples such as Gene, PCA-form2, which is based on the input data (J specifically) gives much faster computations compared to PCA-formL, and also is faster than direct caaputaatioocclssficattiiooo without PCA. In addition, when PCA-forml is used, even though PIC and PIC-reduce are faster than PCA on directly imputed data (DI-reduce), they are still much slower than direct imputation classification without PCA.
286
268
270
272
Interestingly, the accuracy PIC and PIC-reduce are almost identical to PCA on directly imputed data, and are higher than direct imputation classification without PCA. Next, note that the main idea of the proposed methods is to reduce the dimension of the F to speed up the imputation. Therefore, we have made no assumption about the number of features in the missing portion M. In Table and Table q = 15000, 20000, which means 5,531 and 531 missing features in M, respectively. This implies PIC can handle datasets where M has many features.
273
274
276
8

---

Table 6: Five fold CV results (accuracy, speed) of SVM for softlmpute based strategies on the Gene
dataset when y 15000.
missing rate
Strategy
20%
40%
60%
PIC-reduce
(0.994, 2250.451)
(0.992, 2412.082)
(0.992, 2415.434)
PCA-forml
PIC
(0.992, 2429. 114) (0.994, 5018.368)
(0.992, 2276.354)
(0.992, 2284.414)
Di-reduce
(0.994, 4529.766)
(0.994, 3785.947)
PIC-reduce
(0.995, 69.444)
(0.992, 76.393)
(0.992, 85.2)
PCA-form2
PIC
(0.992, 61.451)
(0.992, 68.571)
(0.992, 77.528)
DI-reduce
(0.995, 80.823)
(0.992, 92.265)
(0.994,100.751))
No PCA
DI
(0.985, 71.884)
(0.985, 74.812)
(0.985, 92.309)
Table Five fold CV results (aceuracy, speed) of SVM for softlmpute based strategies on the Gene dataset when = 20000.
missing rate
Strategy
20%
40%
60%
PIC-reduce
(0.994, 2578.910)
(0.994, 4001.717)
(0.994, 3848.950)
PCA-forml
PIC
(0,994, 2583.717)
(0.994, 4144.157)
(0.994, 4057.188)
DI-reduce
(0.995, 2891.994)
(0.994, 4476.563)
(0.995, 4332.869)
PIC-reduce
(0.995, 67.753)
(0.992, 73,884)
(0.995, 81.27)
PCA-form2
PIC
(0.995, 59.815)
(0.995, 66.096)
(0.995, 73,079)
DI-reduce
(0.995, 81.07)
(0.995, 82.407)
(0.995, 91.638)
No PCA
DI
(0.985, 74.06)
(0.985, 71.6)
(0.985, 84.963)
278
8
Conclusion and Remarks
We have presented two novel frameworks for datasets where many continuous features are fully observed. PCAI and PIC, that can speed up imputation algorithms significantly while having com- petitive accuracy MSE/accuracy compared to direct imputation and alleviate the memory issue for some imputation approaches such MICE, kNN. In addition, the frameworks can be used even when some or all of the missing features are categorical or when the number of missing features large. Note that when sample size significantly larger than the number of fully observed features, PCA-form should be used since, in such case, the covariance matrix is much smaller than F. making it faster than PoA-form2. On the other hand, when the number of fully observed features significantly larger than the sample size, PCA-form2 should be preferred, as the covariance matrix bigger than F itself such a case. A limitation of the proposed framework is that there are not many fully observed continuous features, then due to the computational cost of PCA, the proposed frameworks may not lead to any improvement in speed.
280
282
284
286
286
290
Even though PIC is only introduced for classification, the same strategy can be applied to a regression problem. We would like to explore that the future. Moreover, since various dimension reduction techniques such sparse PCA 455, incremental PCA [46), truncated SVD 47 have been developed suit different scenarios, it worth investigating different dimension reduction techniques for PCAT
292
294
and PIC. In addition, it would be interesting to explore if applying PCA variant to the missing partition M would result in even a more efficient method for datasets with continuous features missing partition.
296
298 References
299
[1] Zachary C Lipton, David Kale, Randall Wetzel, et Modeling missing data clinical time series with mns. Machine Learning for Healthcare, 56, 2016.

---

301
[2] Zhengping Che, Sanjay Purushotham, Kyunghyun Cho, David Sontag, and Yan Liu. Recurrent neural networks for multivariate time series with missing values. Scientific reports, 8(1):1-12. 2018.
302
[3] Mostafa Mehdipour Ghazi, Mads Nielsen, Akshay Pai, M Jorge Cardoso, Mare Modat, Sebastien Ourselin, and Lauge Sørensen. Robust training of recurrent neural networks to handle missing data for disease progression modeling. arXiv preprint 1r0.v:180..055000 2018.
305
307
[4] Thu Nguyen, Duy H.M. Nguyen, Huy Nguyen, Binh T. Nguyen, and Bruce A. Wade. Epem: Efficient parameter estimation for multiple class monotone missing data. Information Sciences, 567:1-22, 2021.
308
309
310
[5] S van Buuren and Karin Sosphhuis-Oushhooee mice: Multivariate imputation by chained equations in Journal of statistical software, pages 1-68, 2010.
[6] Jinsung Yoon, James Jordon, and Mihaela Schaar. Gain: Missing data imputation using generative adversarial nets. In International conference on machine learning, pages 5689-5698.
313
PMLR, 2018.
315
77] Ayush Garg, Deepika Naryani, Garvit Aggarwal, and Swati Aggarwal. DI-gsa: deep learning metaheuristic approach to missing data imputation. In International Conference on Sensing and Imaging, pages 513-521. Springer, (2018).
316
318
[8] Thu Nguyen, Khoi Minh Nguyen-Duy, Duy Ho Minh Nguyen. Binh T. Nguyen, and Bruce Alan Wade. Dper: Direct parameter estimation for randomly missing data. Knowledge-Bor -Badee Systems, 240:108082, 2022.
319
320
321
99] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint vrXii:/708.07750 2017.
[10] Daniel J Stekhoven and Peter Bühlmann. Missforest-non conirorest-no---pameetireee missing value imputation for mixed-type data. Bioinformatics, 28(1): 12-118, 2012.
324
325
Jundong Li, Kewei Cheng, Suhang Wang, Fred Morstatter, Robert P Trevino, Jiliang Tang, and Huan Liu. Feature selection: A data perspective. ACM computing surveys (CSUR), 1-55, 2017.
328
327
328
[12] Isabelle Guyon, Jiwen Li, Theodor Mader, Patrick A Pletscher, Georg Schneider, and Markus Uhr. Competitive baseline methods set new standards for the nips 2003 feature selection benchmark. Pattern recognition letters, 28(12):1438-144
329
2007.
[13] Bjørn Grung and Rolf Manne. Missing values in principal component analysis. Chemometrics and Intelligent Laboratory Systems, (2(112):122-11111 1998.
332
333
[14] Alexander llin and Tapani Raiko. Practical approaches to principal component analysis in the presence of missing values. The Journal of Machine Learning Research, 11:1957-2000, 2010.
334
335
[15] Lovedeep Gondara and Ke Wang. Multiple imputation using deep denoising autoencoders. arXiv preprint arXiv: 700.000777077 2017.
336
[16] Vincent Audigier, François Husson, and Julie Josse. Multiple imputation for continuous variables using a bayesian principal component analysis. Journal of statistical computation and simulation, 36(11):2140-2156 2016.
338
[17] Dušan Sovilj. Emil Eirola, Yoan Miche, Kaj-Mikael Björk, Rui Nian, Anton Akusok, and Amaury Lendasse. Extreme learning machine for missing data using multiple imputations. Neurocomputing, 174:220-231, 2016.
341
3/3
[18] Karthika Mohan and Judea Pearl. Graphical models for processing missing data. Journal of the American Statistical Association, pages 1-42, 2021.
344
[19] Trevor Hastie, Rahul Mazumder, Jason D Lee, and Reza Zadeh. Matrix completion and low-rank svd via fast alternating least squares. The Journal of Machine Learning Research, 16(1):3367-3402, 2015.
346
10

---

348
[20]
Rahul Mazumder, Trevor Hastie, and Robert Tibshirani. Spectral regularization algorithms for learning large incomplete matrices. Journal of machine learning research, 11(Aug):2287-2331 2010.
349
351
[21] Sanaz Nikfalazar, Chung-Hsine Yeh, Susan Bedingfield, and Hadi A Khorshidi. Missing data imputation using decision trees and fuzzy clustering with iterative learning. Knowledge and Information Systems, 62(6):2419-2433 2020.
352
354
[22] Md Geaur Rahman and Md Zahidul Islam. Missing value imputation using decision trees and decision forests by splitting and merging records: Two novel techniques. Knowledge-Bode Based Systems, 53:51-65, 2013.
355
357
[23] Lane F Burgette and Jerome P Reiter. Multiple imputation for missing data via sequential regression trees. American journal of epidemiology, 17209):070--076, 2010.
358
359
[24] Shahidul Islam Khan and Abu Sayed Md Latiful Hoque. Sice: an improved missing data
imputation technique. Journal of big data, 7(1):1-21, 2020.
361
[25]
Md Geaur Rahman and Md Zahidul Islam. Missing value imputation using a fuzzy clustering- based em approach. Knowledge and Information Systems, 46(2):389 -22.22 2016.
362
363
[66]
Jared S Murray and Jerome P Reiter. Multiple imputation of missing categorical and continuous values via bayesian mixture models with local dependence. Journal of the American Statistical Association, 11 111(516):1466-1444
364
365
2016.
366
[27]
Collins Leke and Tshilidzi Marwala. Missing data estimation in high-dimensional datasets: A swarm intelligence-deep neural network approach. In International Conference on Swarm Intelligence, pages 259 270. Springer, (2016).
367
368
369
[28] Katarzyna Wožnica and Przemyslaw Biecek. Does imputation matter? benehmark for predictive models. arXiv preprinl arXiv:2007.02837 2020.
[29] Julie Josse, François Husson, et al. Multiple imputation in principal component analysis. Advances in data analysis and classification, 5(3):231-246, 2011.
372
373
[30] Trevor Hastie, Robert Tibshirani, Jerome H Friedman, and Jerome H Friedman. The elements of statistical learning: data mining, inference, and prediction, volume 2. Springer, 2009.
374
[31] Li Qu, Li Li, Yi Zhang, and Jianming Hu. Ppca-based missing data imputation for traffic flow volume: systematical approach. IEEE Transactions on intelligent transportation systems, 10(3):512-522, 2009.
376
377
[32] Alfonso lodice D' D'Ezaa, Francesco Palumbo, and Angelos Markos. Single imputation via chsnk-wise pea. In Conference of the International Federation of Classification Societies, pages 75-82. Springer, 2019.
379
[33]
Abel Folch-Fortuny, Francisco Arteaga, and Alberto Ferrer. Assessment of maximum likelihood pea missing data imputation. Journal of Chemometrics, 30(7):386-393, 2016.
382
383
[34] Vincent Audigier, François Husson, and Julie Josse. principal component method to impute missing values for mixed data. Advances in Data Analysis and Classification, 10(1):5-26, 2016.
384
[35] Robert Ernest Dear. A
missing-dala method for multiple regression models.
386
System Development Corporation, 1959.
387
[36] Darren T Andrews and Peter D Wentzell. Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer. Analytica Chimica Acta, 350(3):34--352, 1997.
389
380
[37] Sam Roweis. Em algorithms for pea and spea. Advances in neural information processing systems, 10, 1997.
[38] Abel Folch-Fortuny. Francisco Arteaga, and Alberto Ferrer. Pea model building with missing data: New proposals and a comparative study. Chemometrics and Intelligent Laboratory Systems, 146:77-88, 2015.
393
11

---

395
[39]
Aude Sportisse, Claire Boyer, and Julie Josse. Estimation and imputation in probabilistic principal component analysis with missing not at random data, Advances in Neural Information Processing Systems, 33:7067-7077, 2020.
396
397
398
[0 Alex Rubinsteyn and Sergey Feldman. fancyimpute: An imputation library for python. https //githu.. wwtp:///aaaaaad//a/cniuptt...eee 2016.
389
[41]
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-leamm Machine learning in Python. Journal of Machine Learning Research, 12:2825-2830, 2011.
401
403
[42] C Okan Sakar, Gorkem Serbes, Aysegul Gunduz, Hunkar C Tunc, Hatice Nizam, Betul Erdogdu Sakar, Melih Tutuneu, Tarkan Aydin, M Erdem Isenkul, and Hulya Apaydin. A comparative analysis of speech signal processing algorithms for parkinson's 's disease classification and the use of the tunable q-factor wavelet transform. Applied Soft Computing, 74:255-263, 2019.
405
407
408
[43] Dheeru Dua and Casey Graff. UCI machine learning repository. 2017.
409
[44] Jiang Li, Xiaowei S Yan, Durgesh Chaudhary, Venkatesh Avula, Satish Mudiganti, Hannah Husby, Shima Shahjouei, Ardavan Afshar, Walter F Stewart, Mohammed Yeasin, et al. Im- putation of missing values for electronic health record laboratory data. NPJ digital medicine, 4()::1-1,,2011
410
412
[45] Rodolphe Jenatton, Guillaume Obozinski, and Francis Bach. Structured sparse principal component analysis. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pages 366-373. JMLR Workshop and Conference Proceedings, 2010.
414
415
416
[46] David A Ross, Jongwoo Lim, Ruei-Sung Lin, and Ming-Hsuan Yang. Incremental learning for robust visual tracking. International journal of computer vision, 77(1): 141, 2008
418
[47] Nathan Halko, Ber-Gunnar Martinsson, and Joel Tropp. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM review, 53(2):217-288, 2011.
419
420
Checklist
421
422
1. For all authors...
423
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
424
contributions and scope? [Yes]. See Table 2 Table 3 Table ??, Table ?? and Section
425
7
(b) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes].
427
428
(c) Did you discuss any potential negative societal impacts of your work? [N/A]
(d) Did you describe the limitations of your work? [Yes]. See the last paragraph of Section
430
431
2. If you are including theoretical results...
432
(a) Did you state the full set of assumptions of all theoretical results? [N/A]
433
(b) Did you include complete proofs of all theoretical results? [N/A]
434
3. If you ran experiments..
435
(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either in the supplemental material or as URL)? [Yes]. The code will be available the form a Github repository upon acceptance, to preserve anonymity.
437
438
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]. See Section 7
439
440
(c) Did you report error bars (e-g., with respect to the random seed after running experi- ments multiple times)? [N/A]
12

---

442
(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes]. See Section 7
443
4. If you using existing assets (e.g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes]. See References list.
(b) Did you mention the license of the assets? [N/A]
447
(c) Did you include any new assets either the supplemental material or as URL? [Yes]
448
The code can be found on a github repository upon the acceptance of the paper.
(d) Did you discuss whether and how consent was obtained from people whose data you're
450
using/curating? [N/A]
451
(e) Did you discuss whether the data you are using/curating contains personally identifiable information offensive content? [N/A]
5. If you used crowdsourcing conducted research with human subjects...
454
(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
455
456
(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
458
(c) Did you include the estimated hourly wage paid participants and the total amount spent on participant compensation? [N/A]
459
13


Reviews:
[{"review_id": "_S-LzJ-iwA", "reviewer": "Reviewer_SAVj", "summary": "The authors present a PCA based framework for missing data imputation specially efficient for high dimensional data. The experiments indicate that the imputation presents low MSE and, when applied to classification tasks, results in similar or better accuracy values.", "questions": "Some details of the proposed algorithms and experiments can be improved:\n\n- Although it is not explicit in the text, I have inferred that the so-called \"partition with missing values\" correspond to features with unknown values (columns of the dataset), instead of samples with unknown feature values (rows of the dataset). Am I correct?\n- In Algorithm 1, how exactly \"R U M\" is handled? Column-wise concatenation?\n- How exactly the missing data was generated? It is not clear if a 20% missing rate is related to 20% instances with a single random missing feature or if it means that 20% of the total features are missing.\n- In the classification experiments, how many data points are used for training and testing? How many independent runs? How hyperparameter selection was performed?\n\nI do not think it is necessary to separate the PCAI and PIC frameworks. It seems to me that PIC is the straightforward application of PCAI on data related to a classification task. Unless I am mistaken, I recommend unifying the presentation of both strategies.\n\nI list additional comments below:\n\n- I believe \"Principal Components Analysis\" is preferred over \"Principle Components Analysis\".\n- Line 117: \"We first conduct dimension reduction on the fully observed partition M...\" -> 'F' is the fully observed partition.\n- Line 151: The matrix 'W' has not been defined at this point.\n- Tab. 4 should include the standard result obtained by the SVM classifier, without PCA.\n- I recommend always including in the supervised experiments the simple baseline of simply removing the instances with any missing data.", "limitations": "The manuscript states sufficiently its limitations.", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The main motivation is relevant and promising. The related work section indicates a well explored field. Nevertheless, the authors should mention and include in the experimental section at least some of the many PCA based approaches to data imputation. See for instance [1,2,3,4] and the references within. Without those comparisons, it is difficult to state the originality of the work.\n\nSince the proposed approach relies on classic PCA and can be coupled with any imputation strategy, it seems to be readily available for practitioners. This is a welcomed advantage of the proposal.\n\nThe writing is mostly sound and the manuscript is well organized. However, some steps of the proposed algorithms are difficult to follow due to the lack of details. I will list them in the next part.\n\nReferences\n\n[1] Qu, Li, et al. \"PPCA-based missing data imputation for traffic flow volume: A systematical approach.\" IEEE Transactions on intelligent transportation systems 10.3 (2009): 512-522.\n\n[2] Folch-Fortuny, Abel, Francisco Arteaga, and Alberto Ferrer. \"PCA model building with missing data: New proposals and a comparative study.\" Chemometrics and Intelligent Laboratory Systems 146 (2015): 77-88.\n\n[3] Folch‐Fortuny, Abel, Francisco Arteaga, and Alberto Ferrer. \"Assessment of maximum likelihood PCA missing data imputation.\" Journal of Chemometrics 30.7 (2016): 386-393.\n\n[4] D’Enza, Alfonso Iodice, Francesco Palumbo, and Angelos Markos. \"Single Imputation Via Chunk-Wise PCA.\" Data Analysis and Rationality in a Complex World (2021): 75.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "S1KV49qfUP4", "reviewer": "Reviewer_wGwK", "summary": "The authors propose we propose a framework based on PCA to speed up the imputation process of many available imputation techniques. The proposed methods are named PCAI and PCA-PIC. Experiments are provided on various datasets.", "questions": "Can the authors explain why the traditional style of imputing on the original missing dataset gives NAs for all missing rates?", "limitations": "The authors addressee adequately the limitaions of  PCAI and PCA-PI.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Weaknesses:\n1) The authors only compared PCAI strategy with the traditional strategy.\n2) \"Principle Component Analysis\" should be \"Principal Component Analysis\"\n\nStrengths:\nThe proposed methods are named PCAI and PCA-PI are novel.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "NQ-iWW6tb6", "reviewer": "Reviewer_BvMn", "summary": "This paper proposes a framework based on principle components analysis (PCA) to speed up the missing data imputation. It divides the feature sets into two partitions -- the fully observed one and the one that contains missing values. The proposed method applies PCA to the fully observed partition to do dimensionality reduction, followed by the existing imputation methods. The authors further propose to apply PCA to the imputed data to speed up the downstream classification task.", "questions": "A suggestion for further improvement: the proposed method only applies PCA to the fully observed partition, yet in many important cases, either we have no prior information about which feature is fully observed, or the feature partition with missing value is very large. If the PCA variant to be proposed could directly apply to the partition with missing values, it would much more interesting. Of course, it has to come with theoretical and empirical validations.", "limitations": "Limitations are not discussed in this paper.", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The paper is overall organized and readers can easily follow.\n\nWeaknesses:\n- The major weakness is that the methodological contribution is quite limited. Projecting data into lower dimensional spaces to speed up downstream tasks is not new. In fact, it has been widely regarded as the go-to tool to handle large datasets.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "FednkHVaIEs", "reviewer": "Reviewer_emZM", "summary": "The authors presented two novel frameworks, PCAI and PIC, that allow for more efficient handling of missing data. There are two use cases, fashion MNIST (imaging data) and Parkinson (voice recording) dataset. ", "questions": "Testing and optimizing imputation is complex and unless one is taking sufficient steps, the results may be biased, and the study will have limited utility and generalizability. \nA comparison of a fashion dataset (in this case imaging data) and a medical dataset (in this case, voice recording) cannot be only about the number of records and number of features. To impute one has to understand the data characteristics, beyond simple statistics. A Deeper discussion of these differences is important if such comparisons are made. ", "limitations": "The main assumption is that introducing random missing is not acceptable unless the author can show that such data suffers from random missing. For instance, clinical data has missing that is not completely random. Please see the paper published in nature digital medicine on this topic. https://www.nature.com/articles/s41746-021-00518-0 \nSimilarly, voice recordings and imaging data suffer likely from non at random missingness due to the nature of the data. ", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength: easy to understand and implement. \nWeakness: The main assumption is that introducing random missing is not acceptable without sufficient evidence and justification. ", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Reject