Detecting incidental correlation in multimodal learning via latent variable modeling
Authors: Taro Makino
Yixin Wang
Krzysztof J. Geras
Kyunghyun Cho
Venue: Accepted by TMLR ()

Abstract: Multimodal neural networks often fail to utilize all modalities. They subsequently generalize worse than their unimodal counterparts, or make predictions that only depend on a subset of modalities. We refer to this problem as \emph{modality underutilization}. Existing work has addressed this issue by ensuring that there are no systematic biases in dataset creation, or that our neural network architectures and optimization algorithms are capable of learning modality interactions. We demonstrate that even when these favorable conditions are met, modality underutilization can still occur in the small data regime. To explain this phenomenon, we put forth a concept that we call \emph{incidental correlation}. It is a spurious correlation that emerges in small datasets, despite not being a part of the underlying data generating process (DGP). We develop our argument using a DGP under which multimodal neural networks must utilize all modalities, since all paths between the inputs and target are causal. This represents an idealized scenario that often fails to materialize. Instead, due to incidental correlation, small datasets sampled from this DGP have higher likelihood under an alternative DGP with spurious paths between the inputs and target. Multimodal neural networks that use these spurious paths for prediction fail to utilize all modalities. Given its harmful effects, we propose to detect incidental correlation via latent variable modeling. We specify an identifiable variational autoencoder such that the latent posterior encodes the spurious correlations between the inputs and target. This allows us to interpret the Kullback-Leibler divergence between the latent posterior and prior as the severity of incidental correlation. We use an ablation study to show that identifiability is important in this context, since we derive our conclusions from the latent posterior. Using experiments with synthetic data, as well as with VQA v2.0 and NLVR2, we demonstrate that incidental correlation emerges in the small data regime, and leads to modality underutilization. Practitioners of multimodal learning can use our method to detect whether incidental correlation is present in their datasets, and determine whether they should collect additional data.

Published in Transactions on Machine Learning Research (08/2023)
Detecting incidental correlation in multimodal learning via latent variable modeling
Taro Makino
toro toro@nyu.ed
NYU Center for Data Science
Yixin Wang
girimw@eumich.edd edu
University of Michigan
Krzysztof J. Geras
h.j-geras@myu.cd
NYU Grossman School of Medicine
Kyunghyun Cho
kyunghyun.cho cho Wny.. edu
NYU Center for Data Science
Prescient Design, Cenendech
CIFAR LMB
Reviewed on OpenReview: https: // optp///vee...vee...mm net/ forum? id= 9QmDr
Abstract
Multimodal neural networks often fail to utilize all modalities. They subsequently gener- alize worse than their unimodal counterparis, or make predictions that only depend on a subset of modalities. We refer to this problem as modality underutilization. Existing work has addressed this issue by ensuring that there are no systematic biases in dataset creation, or that our neural network architectures and optimization algorithms are capable of learn- ing modality interactions. We demonstrate that even when these favorable conditions met, modality underutilization can still occur in the small data regime. To explain this phenomenon, put forth concept that we call incidental corvelation. It is spurious correlation that emerges in small datasets, despite not being a part of the underlying data generating process (DGP). We develop our argument using DGP under which multimodal neural networks must utilize all modalities, since all paths between the inputs and target are causal. This represents an idealized scenario that often fails to materialize. Instead, due to incidental correlation, small datasets sampled from this DGP have higher likelihood under an alternative DGP with spurious paths between the inputs and target. Multimodal neural networks that use these spurious paths for prediction fail to utilize all modalities. Given its harmful effects, we propose to detect incidental correlation via latent variable modeling. We specify an identifiable variational autocncoder such that the latent posterior encodes the spurious correlations between the inputs and target. This allows us to interpret the Kullback-Leibler divergence between the latent posterior and prior as the severity of incidental correlation. We use an ablation study show that identifiability important in this context, since we derive our conclusions from the latent posterior. Using experiments with synthetic data, as well as with VQA v2.0 and NLVR2, we demonstrate that incidental correlation emerges in the small data regime, and leads to modality underutilization. Prac- litioners of multimodal learning can use our method to detect whether incidental correlation present in their datasets, and determine whether they should collect additional data.

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Published in Transactions on Machine Learning Research (08/2023)
1 Introduction
Multimodal learning refers to jointly modeling data from different modalities, such images, speech, and
text (Ngiam et al.] 2011 Baltrusaitis et al.
2019
Liang et al.
2022 While the goal is to learn modality
interactions that are useful for downstream tasks, multimodal neural networks often generalize worse than
their unimodal counterparts (Jabri et al.
Poliak ct al. 2018 Jean & Cho 2019 Wang et al., 2020a; Wu et al.) 2020 2022,, or make predictions that only depend on a subset of modalities (Agrawal et al. 2016 Goyal al. 2017 Agrawal al.
2016
2018 Cadène al. 2019 Hessel & Lee 2020). Since these are
both symptoms of multimodal neural networks failing to utilize all modalities, we treat them the same problem, and refer to it modality underutillzation.
Existing work has addressed this issue by ensuring that there are no systematic biases in dataset cre- Suhr et al. 2019 Hudson & Manning, 2019), or that our neural network architectures and optimization algorithms are able to learn modality interactions (Hazirbas et al.
ation (Goyal et al.) 2017 Poliak et al. 2018
2017 Zeng et al., 2019 Song al. 2020 Valada al.) 2020 Wang al., 2020a by Wu et. al. 2022). We demonstrate that even under these favorable conditions, modality underutilization can still occur in the small data regime. This has important implications for praclitioners of multimodal learning, Even if they carefully design their data collection procedure to be free of biases, and use proven neural network architectures and optimization methods, they are still vulnerable to modality underutilization if they do not collect enough data.
We explain this phenomenon using a concept that we call incidental correlation. Incidental correlation is a spurious correlation that emerges in small datasets, despite not being a part of the underlying data generating process (DGP). For example, suppose the ground-truth DGP consists of two independent Bernoulli random variables. If we sample small dataset from this DGP and compute the correlation between the variables, it is likely to be significantly different from zero. In other words, the dataset has higher likelihood under the alternative DGP than under the ground-truth DGP that it was sampled from.
To connect this idea to modality underutilization, we put forth an idealized DGP under which modality underutilization cannot occur. We then explain how this ideal scenario breaks down in the small data regime. The DGP a causal graphical model (Pearl] 2009),, since we consider the causal relationships between the variables. There is an unobserved variable that gives rise two observable input modalities and x'. These input modalities then cause the target y. We refer to this DGP the multimodal generating process (MGP), and show its graph in Fig. la Under the MGP, we have
ply do(x)) p(y x,xx).
(1)
In causal language, p(y do(x), do(x')) )) is identifiable, meaning that obtainable by estimating p(y x, x') from observational data. Therefore, if we estimate p(y x, x') and use to predict the target given the inputs, the prediction is purely based on the causal paths x y and x' + y. Such a model successfully utilizes all modalities.
u
x'
(a) Multimodal generating process (MGP). All paths between the inputs and target are cansal.
(b) Spurious gemerating process (SGP). The edge from to y unblocks spurious paths be- tween the inputs and target, which lead to modality underutilization.
Figure
We argue that modality underutilization occurs when this ideal scenario fails materialize. Suppose we sample small dataset from the MGP, where and y conditionally independent, given the inputs. Due
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to incidental correlation, our dataset can have higher likelihood under an alternative DGP with an edge from to y. This additional edge makes u and y conditionally dependent given the inputs. We call this alternative DGP the spurious generating process (SGP), and show its graph in Fig. [b] The edge from u to y unblocks the spurious paths x < u u-y y and x' + u u y, and prevents Eq. I from holding. Consequently, if we estimate p(y x, x') and use it to predict the target given the inpuls, we can no longer tell whether the predictions are based on the causal paths, or the spurious oncs. This ambiguity can lead to modality underutilization. For example, model can rely solely on the spurious path x u y for prediction, thus failing to utilize the x' modality.
It is beneficial to detect incidental correlation, given that it leads to modality underutilization. The main challenge in doing so is that it involves the unobserved variable u. We circumvent this difficulty by using latent variable modeling. We an identifiable variational autoencoder (VAE) (Kingma & Welling 2014) such that the relationship between the latent. variable z and the inputs captures the incidental correlation between u and the target. This allows us to interpret the Kullback-Leibler (KL) divergence between the latent posterior and prior as the severity of incidental conrelation. We elaborate on this procedure in Sec. A Since we derive our conclusions from the latent posterior, it is important to prevent learning arbitrary latent space. We therefore use a VAE with mixture prior and a piccewise affine decoder to achieve identifiability (Kivval et al. 2022). In order to assess its importance, we compare these results to those derived using a vanilla VAF Kingma& & Welling 2014,, which is unidentifiable. Our ablation study demonstrates that identifiability is necessary for drawing correct conclusions.
We conduct experiments to empirically verify our main claim, which is that even if the underlying DGP is free of systematic biases, incidental correlation emerges in the small data regime, and leads to modality underutilization. Our experiments consist of toy problem with synthetic data and small neural networks, as well as realistic settings with VQA v2.0 (Goyal et al. 2017) and NLVR2 (Suhr et al., 2019). and a state-of-the-ar model called FIBER (Dou et al.) 2022). In all cases, our experiments consist of two stages.
The first stage shows that even when incidental correlation is absent in the large data regime, it emerges as we reduce the size of our datasets. We do this by training a VAE, and showing that the KT. divergence between the latent posterior and prior is approximately zero for large datasets, and increases as the datasets become smaller. This occurs because the latent variable encodes spurious correlations between the inputs and larget that are present in small datasets, and lead the latent posterior to diverge from the prior.
The second stage demonstrates that the emergence of incidental correlation leads to modality underutiliza- tion. To show this, we train a multimodal neural network and an ensemble of unimodal neural networks, and use their generalization gap as a proxy for modality underutilization. The multimodal neural network generalizes better than the unimodal ensemble in the large data regime, but this difference crodes as the datasets become smaller. We attribute this to spurious paths between the inputs and target that fail to generalize.
Practitioners of multimodal learning can use our method to detect whether incidental correlation is present in their datasets, and determine whether they should collect more data. This is useful in realistic situations, when practitioners encounter modality underutilization in data-constrained settings. While our experiments involve a large dataset, this was for the purpose of experimental control. We showed that even when incidental correlation is absent in the large data regime, it emerges when we reduce the size of our datasets. Data is less abundant. in many real-world applications, and this is where our method provides value.
2 Related work
2.1 Modality underutilization
Modality underutilization is a long-standing open problem, and existing work has generally addressed it from two different directions. The first direction is to ensure that there are no systematic bias in dataset creation. This is motivated by the fact that many benchmark datascts intended to require multinodal reasoning could unwittingly be solved with a subset of modalities. Poliak et al. (2018) showed in natural language inference that tasks designed to require the use of hypothesis and a context could be solved with hypothesis-only
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baselines. A similar problem occurs in visual question answering (VQA) (Antol al. 2015 Instead of answering question about specific image, VQA models often predict the same answer for given question across a wide variety of images (Agrawal et al. 2016 Jabri et al., 2016 Agrawal et al. 2018 Cadène et al. 2019). To counter this problem, many multimodal benchmark datasets have been proposed that are carefully constructed to be free of systematic biases (Goyal el. al. 2017; Hudson & MManning 2019). We show that this precaution is not enough, and that incidental correlation can be detected in such datasets the small data regime.
The second direction is to ensure that our neural network architectures and optimization algorithms are capable of learning modality interactions. In terms of neural network architectures, the majority take into account the idiosyncrasies of the specific modalities and prediction tasks (Hazirbas et al. 2017 Zeng et al.
2019 Song et al. 2020; Valada et al. 2020 Wang et al., 2020b), but generic approaches also exist (Jean & Chol 2019 Baevski al. 2022). Regarding optimization algorithms, Wang et al. (2020a) proposed to mitigate modality underutilization by averaging gradients across modalities, while Wu et al. (2022): Sun et al. (2021) took the approach of balancing the modality-specific learning rates. Meanwhile, Gat. al.
(2020) introduced regularization term based on functional entropy to balance the contributions of each
modality.
2.2
Modeling unobserved confounding
Our work is related to causal inference approaches that address unobserved confounding between multiple
treatments and a single outcome (Wang et al. 2017 Frot et al.
2018 Tran & Blei 2018 Heckerman 2018
Janzing & Schölkopl 2018; Wang & Blei 2019
Ranganath
Perotte 2018
D' D'Amour 2019 Cevid et al.
2020 Puli et al.) 2020: Agrawal et al., 2021 Wang & Blei (021). These studics leveraged the correlations
among the multiple treatments observable signatures for inferring the shared unobserved confounder. We also draw inspiration from Makino et al. (2022). who adjusted for unobserved confounding in the context of
multitask learning, where there is a single input and multiple targets.
2.3 Identifiable latent variable modeling
Informally, a latent variable model is identifiable if the true joint distribution over the observed and latent variables can be learned from data. The precise definition is context-dependent, and we provide ours in the appendix. Identifiablity is important in the context of this work, since we derive our conclusions from the latent posterior. The theory originated in nonlinear ICA (Hyvärinen & Morioka 2016 2017 Hyvärinen let al.) 2019),, which was extended to VAËs in Khemakhem et al. (2020). These works assumed there is observed auxiliary variable that the latent prior factorizes over, such a timestamp or class label.
Since auxiliary variables are not always available, there have been elforts to relax this requirement. Wang
lt al. (2021) achieved this with Brenier maps and input convex neural networks, and [Moan et al. (2022)
did so using & sparse model in which each dimension of the observed data depends on a small subset of the latent variables. There also exist approaches based on the principle of independent mechanisms from
causality (Gresele et al. 2021 Lachapelle et al.] (022). We adopt the assumptions of Kivva et al. (2022) who achieve identifiability without auxiliary information via a mixture prior and a piecewise alfine decoder. This approach is appealing to us because it is consistent with conventional modeling choices that scale to nigh-diimnsional data (Jiang et al., 2017 Falck et al.) 2021). It has also been shown to perform well in terms of various empirical measures of identifiabiiity (Willetts & Paige 2021). The topic of identifiability is also related to disenlangleement, which can be thought of as identifiability up to permutation and component-wiss
transformation (Higgins et al. 2017 Li & Mandt 2018 Locatello et al., 2019 Bengio et al.) 2020 Bai et al.
2021
Lachapelle et al., (2022). Our work also joins a direction of rescarch that demonstrates the practical
utility of identifiability. While this topic has been relatively unexplored (Hyvärinen et al. 2023). Lopez et al. demonstrated its importance for modeling single-cell genomics data.
2023
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3 Incidental correlation
We explain modality underutilization using a concept that we call incidental correlation. We define this as a spurious correlation that emerges in the small data regime, despite not being a part of the underlying DGP. Small datasets that are sampled from the MGP; where u and y are conditionally independent given the inputs, can have higher likelihood under the SGP, where this independence does not hold. In the SGP, the correlation between the inputs and targets flow through the causal paths + y and x' + y, as well the spurious paths x u - y and x' + u- y. As we discussed in Sec. 1 these spurious paths contribute to modality underutilization.
The severity of this effect depends on the degree to which u and y are conditionally dependent given the inputs. In order to explain this, let us define in the SGP as
y = g((),,)
(2)
where by is exogenous noise, and ( is function that determines the degree to which u and y are conditionally dependent given the inputs. On one extreme, if g(u) is constant function, u and y are conditionally independent given the imputs. This makes the SGP equivalent to the MGP. On the other extreme, if g(u) y, u and y are perfectly dependent given the inputs. In this case, u and y collapse into a single variable, which we refer to as y. In the corresponding graph shown in Fig. Pa the edges between the inputs and target are bidirectional, forming a Markov random field. The data distribution is given by
x(x,x', x') y) oc exp(ox(x)) + ox (x') + dy(y) + (xy(xxy) ox (xx yy).
where the o's are potential functions. Under this distribution, the prediction for y is given by
arg max (y) + (x, + (x'r(x',
If (y) is uniform, and thus constant with respect to y, this corresponds to ensemble of the two unimodal neural networks (x, y) and Φx (x,))) In other words, multimodal learning is equivalent to unimodal ensembling in this particularly degenerate case of the SGP. In practice, the severity of incidental correlation is likely to fall somewhere between these two extremes.
x
x
x
(a) When u and y collapse into a single variable which we call y, the graph becomes Markov random field because the edges between the in- puls and larget are bidirectional.
(b) Selection bias induced by conditioning on the collider S, which makes and y condition- ally independent given the inputs.
Figure
Incidental correlation is not the only way that and y can become conditionally dependent given the inputs. Another way this occur is due to selection bias, where there is an additional node S E { that represents selection criteria (Bareinboim & Pearl 2012). We show the corresponding graph in Fig. 2b Data is sampled from a DGP, and is included in the dalasel when 5 = 1. Since S is a child of and y, this induces a collider bias and makes u and y conditionally dependent given the inputs. Selection bias is an example systematic bias, so we do not consider it this work. While systematic biases are indood problematic, the purpose of our work is show that even under favorable conditions where there are no systematic biases, modality underutilization occur in the small data regime due to incidental correlation.
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4 Detecting incidental correlation
(())) Supposc we have a multimodal datasct D = (x(*), x'(m), y Jn=i: where N is the size of the datasct. It is beneficial to be able to detect whether incidental correlation is present in D, since if it is, spurious correlations between the inputs and target can lead to modality underutilization. We propose to detect
incidental correlation using latent variable modeling.
Our method is based on the following high-level idea, which we elaborate on in the following paragraphs. If there is no incidental correlation in D, then it has highest likelihood under the MGP, and (x,x') is sufficient for predicting the target. In contrast, if incidental correlation is present, D has higher likelihood under the SGP, and {x,x'} } is no longer sufficient for predicting the target. We therefore introduce latent variable z, and predict the target based on {x, x', 2). 2 encodes any additional information that is useful for predicting the target, given the inputs. This additional information corresponds to the spurious correlations between the imputs and target.
To achieve this, we specify a conditional VAE (Kingma & Welling 2014 Kingma et al. 2014 Sohn et al. 2015) with encoder q(z x. x,x',x y) and decoder ply x, x, 2), and maximize the lower bound of log p(y x,x'). ), which is
E gt/xx (y)gg xx,x, x)] D (xz( | x,x',)) |l p(z)).
(3)
This is called the evidence lower-bound (ELBO), and is derived in the appendix. The KL term in the ELBO acts as a regularizer, and discourages putting information in unless necessary. This mcans that if there are no spurious correlations between the inputs and largets, the encoder does not need to do anything, and the KT, term is driven to zero. However, if incidental correlation is present in D, then the spurions correlations between the inputs and target are represented by z, and the KL term increases. We can therefore interpret the KL divergence between the latent posterior and prior as the severity of incidental correlation. Another way interpret this is as conditional independence test. We are using the KT, term to determine whether u and y conditionally independent given the inputs, without having to observe u.
If the KL divergence between the latent posterior and prior is close to zero, this leads us to conclude that incidental correlation is absent. from D. In order to prevent false negatives, we need to take precautions to avoid a common failure mode of VAEs called posterior collapsc. Posterior collapse refers to the latent pos- terior being independent of the data, and equaling the prior. This has often been attributed to optimization issues specific VA (Dieng et al. 2019 Lucas et al. 2019 Razavi et al. 2019),, but was linked to latent variable identifiability by [aann et al. (2021) Posterior collapse is not possible when the true model does not exhibit posterior collapse, and is identifiable up to invertible affine transformation. In the context of an observed variable x and latent variable 2, Wang et al. (2021) defined unidentifiability as p(x z) = p(x), and posterior collapse as p(z x) p(z). The authors showed that the former implies the latter. Conversely, if the true model satisfics p(x z) + p(x), then its posterior does not collapsc. If we estimate the true model up to an invertible affine transformation, then p(x 2) * p(x) holds for our model, and its posterior does not collapse. In other words, non-collapsed posterior cannot be transformed into collapsed posterior by an invertible affine transformation.
Therefore, we adopt the issumptions of Kivva et al. 2022 to achieve identifiability up to an invertible alfine transformation. Informally, the two assumptions are that that the latent prior is a Gaussian mixture, and that the decoder is piecewise affine. In the appendix, we state the relevant assumptions and identifiability results of Kivva et al. (2022). The latent prior is given by
K
p(z) = Σ
Pc: Ec).
k=1
where K is the number of components, and C' is a categorical variable. The corresponding graph is shown in Fig. 3
A key requirement in specifying our model that and y are conditionally dependent given (x, x',' since this is what allows us to model incidental correlation with the latent posterior. This can also be achieved
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x
x'
Figure 3: Our VAE has a mixture prior over z, where C is the mixture component.
with an alternative model with edges from to {x,x'). These edges are present in the SGP, as seen in Fig. Ib However, it is unnecessary to include these edges in model, since {x,x'} are always conditioned on. The only unblocked path from z to y conditioned on (x,x²} is the edge from z to so we chose to make z to fx,x²} } marginally independent in our model. This has the practical benefit of simplifying the implementation of the KL divergence between the latent posterior and prior.
To summarize, we train an identifiable VAE in order to detect incidental correlation, where the latent posterior encodes the spurious correlations between the inputs and target. This allows us interpret the KL divergence between the latent posterior and prior as the severity of incidental correlation. This value should be zero when datasets have higher likelihood under the MGP relative to the SGP, since the inputs are sufficient for modcling the target. However, this value will be positive if, due to incidental correlation, there is additional spurious information that is predictive of the target.
There are three conditions under which we are correct to interpret the KL divergence between the latent posterior and prior as the severity of incidental correlation. First, our causal graph in Fig, LB correctly describes the true DGP, then any information in addition xx,x') that is useful for predicting y spurious. Second, if the VAE is identifiable, the latent posterior represents this spurious information. Third, the VAE is trained until convergence, the KL term is minimized, meaning that it is only positive when the spurious information is present.
5 Experiments
5.1 Toy problem
We begin by verifying our claims with a toy problem with synthetic data. Our toy problem is designed that in the large data regime, multimodal learning successfully utilizes all modalities. We then reduce the size of the dataset, while keeping everything else the same. This gradually induces incidental correlation, which subsequently leads to modality underutilization.
The prediction task is inspired by the exclusive or (XOR) operation. XOR is logical connective that outputs true exactly one of two imput conditions is true. It is relevant from the perspective comparing multimodal and unimodal learning, because knowing only one of the two input conditions bears no information on the output value. The DGP is
N(O,1),
x N(u, + 1,001),
x' ~ N(u
Y = -1000 x')),
where u E 2D x, x' E ERD, and Y E 10. Here, we set b = 1.5 and a 0.1, and provide additional results with b 6-3 3 and = 1 in the appendix.
The mean of x a random subset of u that is offset by 1- This offset serves an important purpose, which we claborate on in the next paragraph. The set of indices are a randomly sampled half of the full set of indices f1....,D), We denote the remaining half of indices as -J .......D) \ J. This DGP is an MGP, since the target is defined without involving Since its definition includes interaction between all
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modalities, classifying the target requires using all modalities. However, as we will show, spurious solution emerges in the small data regime due to the randomness of sampling.
In order to explain this visually, we illustrate the prediction task in Fig. in the simplest setting with scalar 1. As seen in Fig. da in the large data regime, a multimodal neural network can learn predict Y = when the inputs have the same sign, and Y = otherwise. In contrast, a unimodal ensemble cannot express this decision rule because it considers each input separately. Therefore, multimodal learning generalizes better than unimodal learning in the large data regime. Fig. sboshows that the situation changes in the small data regime. Since offset the mean of X by b == 1.5, unimodal neural network accurately classify Y while only looking at X' Therefore, the predictive advantage of multimodal learning over unimodal learning deteriorates in the small data regime.
inputs, ie.
0
X
-2
0 5
0
Y= 0
Y=1
Y=
Y=1
(a) In the large data regime, both modalities are required in order to classify the target.
(b) In the small data regime, the targel be classified using single modality.
Figure 4: Toy problem with scalar inputs.
In the following experiments, we sample several datasets from the DGP that vary only in the number of examples N E {100, 400, 1600, 6400, 25600}. We then randomly select 60% as the training set, 20% as the validation set, and the remaining 20% as the test set. We train for a certain mumber of epochs M that depends on N, and early stop when the validation loss does not improve for [0.1 M] epochs. table with the values of M and N the appendix. We use a batch size of 128 for all experiments. We show the results for D here, and those for D 16 in the appendix. For each N, we train ten models starting from different randomly-initiiaiized parameters, and report the mean and standard deviation.
5.1.1 Detecting incidental correlation with observed
We detect incidental correlation in two ways: using a simple heuristic with u observed, and with our VAE- based detection method described in Sec. | where u unobserved. In both cases, we show that incidental correlation emerges in the small data regime. The following heuristic with u observed serves as sanity check, since if cannot detect incidental correlation with u observed, we should not be able detect it when it is unbseeved. We define alternative DGP where Y is redefined as
Y (rx( TX u)).
This alternative DGP a SGP, since there is an edge from u to Y. We then compute
N
arg max Σ
log (m)
(m))) a (()
n=1
on the training set, and report the value of ||a|]] corresponding to the maximum log-likelihood on the validation set. The only trainable parameter is E R22D which we optimize using the Adam optimizer (Kingma & Ba 2015) with a learning rate of 10-3
Since D was sampled from an MGP, where u and are conditionally independent given the inputs, a Tu should play part in maximizing the likelihood. Therefore, we can interpret ||o|]| as the degree of incidental
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correlation. The results are shown in Fig. 5a As expected, ||a]| is centered near zero in the large data regime, and increases the dataset becomes smaller. This confirms that incidental correlation emerges in the small data regime.
0.03
0.02
33 0.5
0.01
0.0
0.00
100
400
1600
6400
25600
100
400
1600
6400
25600
Dataset size
Dataset size
Identifiable
Unidentifiable
(a) With observed, the of the optimal a increases as we reduce the size of the datasel.
(b) With unobserved, the KL divergence be- tween the latent posterior and prior increases as we reduce the size of the dataset. This pat- tern is more discernible with the identifiable VAE.
Figure 5: Detecting incidental correlation the toy problem with D 1, b= 1.5, and 0.1. Reducing the size of the dataset makes incidental correlation emerge, both when is observed and unobserved.
5.1.2 Detecting incidental correlation with u unobserved
Given the success of our sanity check with u observed, we move on to detecting incidental correlation with our VAE-based method, where u is unobserved. Our VAE consists of an encoder and a decoder, which are both implemented using MLPs with two hidden layers with 128 neurons each, and ReLU activations. This choice of activation function in the decoder satísfies assumption for achieving identifiability (Kivva ct al. 2022). We additionally train vanilla VAE (Kingma & Welling 2014) with the same hyperparamoters except for sigmoid aclivations in the decoder, which violates the assumptions of Kivva et al. (2022). We refer to this as the unidentifiable VAE. This ablation study allows us to check whether identifiabllit helps us draw correct conclusions based on the latent posterior.
The two VAFs have the same encoder, and their decoder also the same except for the choice of activation function. Their biggest difference is in their prior over the latent variable z E 1 For the encoder, two MLPs each take as input the concatenation of fx, xx,x', y) and return the mcan and covariance parameters of the multivariate Gaussian distribution gz x, x,'', y). For the decoder, MLP takes as input the concatena- tion of (x, x', 2} and outputs the values of the categorical distribution ply x, 2). As for the prior, in our identifiable VAE, we use a Gaussian mixture prior to satisfy an assumption from Kivva et al. (2022). There are 16 mixture components, where each component is Gaussian with diagonal covariance. The mixture com- ponents are uniformly initialized, and the Gaussian parameters are Xavier normal initialized. All parameters of the mixture prior are updated during training. The prior our unidentifiable VAE Gaussian with zero mean and unit covariance. The parameters of the prior are updated during training for the identifiable VAE. but not for the unidentifiable VAE. Both VAEs are trained with the Adam optimizer (Kingma & Ba. 2015 with a learning rate of 10-4
Our results in Fig. 5b show that for the identifiable VAE, the KL divergence bet the latent posterior and prior centered near zero in the large data regime, but increases as the dataset becomes smaller. This means that incidental correlation emerges the small data regime, as we expected. This relationship does not hold for the unidentifiable VAE, whose posterior collapses. This supports the theory of Kivva et al. (2022), and confirms the importance of achieving identifiability when drawing conclusions based the latent posterior.
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5.1.3 Comparing multimodal and unimodal learning
Having detected incidental correlation, we move on to comparing multimodal and unimodal learning in its presence. Our multimodal neural network implemented using an MLP which takes as imput the concatenation of {x,x') x'), and outputs the values of the Bernoulli distribution p(y x, x,x'). The ensemble of unimodal neural networks consists of two MLPs. The MLPs separately take input and x', and
output the values of p(y x) and ply x'). These unimodal predictions averaged to form the ensemble prediction. All of these MLPs have two hidden layers with 128 neurons each, and ReLU activations. They are trained with the Adam optimizer (Kingma & Ba 2015) with learning rate of 10-3.
We interpret the difference in log-probability of the target given the inputs between the multimodal neural network and the unimodal ensemble as a proxy for modality underutilization. We refer to this difference as the generalization gap, and use it as the vertical axis in our results in Fig. G Our results show that the multimodal neural network generalizes better than the unimodal ensemble in the large data regime, but this difference erodes when datasets become smaller. This serves strong evidence that incidental correlation contributes to modality underutilization.
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Figure 6: Comparing multimodal and unimodal learning the toy problem with D 1, b 1.5, and = 0.1. Multimodal learning generalizes better than unimodal learning in the large data regime, but the difference narrows as we reduce the size of the dataset.
5.2 VQA v2.0 and NLVR2
Having verified our claims on the toy problem, we move realistic settings with two popular benchmark visual language datasets called VQA v2.0 (Goyal et al.) 2017) and NLVR2 (Suhr et al. 2019), and state-of- the-art neural network architecture called FIBER (Dou et al. 2022). Both of these datasets are designed to be less systematically biased than their respective first iterations. Therefore, they represent ideal test beds for us to demonstrate that incidental correlation can occur in the absence of systematic dataset biases.
Similar to our experiments with the toy problem, our experiments in this section consist two stages, where we first detect the presence of incidental correlation, and then compare the generalization gap between multimodal and unimodal learning.
VQA v2.0 We experiment with VQA v2.0 (Goyal et al., 2017,, which is revised version of VQA v1.0 (An- tol et al., 2015) that constructed be free of systematic biases. Models trained on VQA v1.0 were frequently observed to ignore the image when answering a question. This is thought to occur because the dataset exhibits strong correlations between the questions and answers. To remedy this, the authors of VQA v2.0 ensured that each question in the dataset is associated with a pair of similar images that result in two different answers.
The dataset consists of images and questions as the inputs, and answers as the target. Each target is a vector representing the 3, 129 most common answers in the training and validation sets. Each element of this vector represents an answer, and the values are in [0, 1] to reflect the labelers' uncertainty. The bog-probability of the target is the sum of log-probabilities of the individual answers. This reflects standard practice when working
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with this dataset. We construct several versions of the dataset that vary only in their number of examples. To do so, we first merge the training and validation set to use as the full set of examples. We do not include the test set, because the ground-truth labels are not publicly available for it. The creators of the dataset indexed these examples in terms of unique images, where cach image is associated with a variable-sized set of questions and answers. To sample dataset, we randomly sample N E (500, 2000, 8000, 32000, 128000} unique images from the full set of 217,522, and split them into training, validation, and test sets, using a 60%, 20%, and 20% split. Thus, the dataset sampling procedure is consistent across all choices of N. Similarly to the toy problem, in the following experiments we train for certain number of epochs M for a given N, whose value are provided in the appendix. In all cases, we early stop when the validation loss stops improving for 20 epochs. We use batch size of 512 for all experiments. For each N, we train five models from different random initializations, and report the mean and standard deviation.
NLVR2 We additionally experiment with NLVR2 (Suhr et al. 2019), which is designed to be less sys- lematically biased than NLVR (Suhr et al.] 2017 its previous iteration. NLVR2 represents the binary classification task of answering true or false question regarding pair of images. Therefore, there are three inputs, where two are images and one is text. We merge the training, validation, and test examples together, for a total of 59,677. We then randomly sample N E {200, 800, 3200, 12800, 51200} examples from the full set, and split. them into training, validation, and test sets again using a 60%, 20%, and 20% split.
For both datasets, instead of processing the raw image and text inputs, we instead use the embeddings produced by a ththe-tf neural network called FIBER (Dou et al., 2022) that was pretrained on a diverse set of datasets and tasks. We use version of the model that was released by the authors that uses a Swin Transformer as the image backbone (Liu et al. 2021 and RoBERTa as the text backbone (Liu et al., 2019). The image and text embeddings are both in R For VQA v2.0, we denote the image embedding as x, and the text embedding as x'. For NLVR2, we denote the two image embeddings as and x2, and the text embedding as x'. During training, we freeze the weights of the image and text backbones that produce the embeddings.
5.2.1 Detecting incidental correlation
In order to detect incidental correlation, we train identifiable and unidentifiable VAEs, and report the KL divergence between the latent. posterior and prior the test set, using the weights that minimize the validation loss. The VAEs have encoders and decoders that both implemented using MLPs with two hidden layers with 512 neurons each. The MLPs are parameterized with ReLU activations, except for the decoder of the unidentifiable VAE, which uses sigmoid activations. The choice of sigmoid activations leads the unidentifiable VAE to violate the piecewise affine decoder assumption in Kivva et al. (2022). For both VAEs, the latent variable z is in R512, The identifiable VAE has a mixture prior with 128 components, where each component is Gaussian with diagonal covariance. Both the categorical distribution over the components, and the mean and diagonal entries of the components are randomly initialized and updated during training. The components are uniform initialized, and the Gaussian parameters are Xavier normal initialized. The prior for the unidentifiable VAE is Gaussian with mean zero and unit covariance, and its parameters are not updated during training. Both VAEs are optimized with the Adam optimizer (Kingma & Ba 2015 with a learning rate of 10-4.
In Fig. 7 we show our results for detecting incidental correlation VQA v2.0 and NLVR2. The conclusions are similar to what we saw for the toy problem. With the identifiable VAE, the KL divergence between the latent posterior and prior is close to zero in the large data regime. This implies that the dataset is consistent with the MGP, where there are spurious paths between the inputs and targets. However, the KL term increases as we reduce the size of the dataset. This is because small datasets have higher likelihood under the SGP, where there are spurious paths between the inputs and target. These spurious correlations are encoded into the latent posterior, making it diverge from the prior.
In contrast, the results with the unidentifiable VAE are unclear. For both VQA v2.0 and NLVR2, the posterior of the unidentifialle VAE collapses when it does not for its identifiable counterpart. Also, the non- monotonicity of the KT. term with respect to dataset size makes detecting incidental correlation diffieult.
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Similar to the toy problem, these results support the theory of Kivva et al (2022) and demonstrate that identifiability is critical when drawing conclusions based on the latent, posterior.
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Results on VQA v2.0 and NLVR2 for detecting incidental correlation. Incidental correlation emerges in the small data regime, and this pattern is more discernible with the identifiable VAE.
Figure 7:
5.2.2 Comparing multimodal and unimodal learning
We compare how multimodal neural network generalizes relative to unimodal ensemble. This gencralization gap is a proxy for modality underutilization. For both datascts, the multimodal and unimodal neural networks are implemented as MLPs with two hidden layers with 512 units each, and ReLU activations, which are trained with the Adam optimizer (Kingma & Ba 2015 with a learning rate of 10-4
For VQA v2.0, the multimodal neural network takes the concatenation of {x, x'} and outputs logp(y x, x.).. Since there are three inputs in NLVR2, the multimodal neural network takes in the concatenation of X2, {x1,X2; x') and outputs log X1,X2, x'). The unimodal ensemble for VQA v2.0 consists of two MLPs that separate take in x and x', and output p(y x) and p(y x'). Similarly, for NLVR2, three MLPs take in X1, X2 and x', and output p(y x1), p(y X2), and ply x'). In both cases, the ensemble output is the log of the average of the unimodal outputs.
Our results in Fig. show that for both VQA v2.0 and NLVR2, the multimodal neural network gencralizes better than the unimodal ensemble the large data regime. This represents the ideal setting where mul- timodal learning works as intended. However, datasets become smaller, multimodal learning no longer generalizes better than the unimodal ensemble. This is because incidental correlation makes the inputs and target spuriously correlated, and the multimodal neural network learns to predict the target using these spurious paths.
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Figure 8: Results VQA v2.0 and NLVR2 for comparing multimodal and unimodal learning. The gener- alization gap between multimodal and unimodal learning narrows in the small data regime.
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6 Conclusion
We have demonstrated using both synthetic and real data that incidental correlation emerges in the small data regime, and leads to modality underutilization. The most important takeaway is that when pursuing multimodal learning, it is not enough to just worry about systematic dataset biases, or neural network architectures and optimization algorithms. Our results show that even in an ideal setting where these concerns are met, and multimodal neural networks should successfully utilize all modalities, they fail to do in the small data regime. In addition to the existing concerns, must also acquire sufficient amount of data in order for multimodal learning to be successful. When data is scarce, it may be futile to try to improve multimodal Icarning without resolving the issue of incidental correlation. Our proposed method enables practitioners to check whether incidental correlation is present in their datasets, and determine whether they need to collect more data.
So far, we have reported the issue incidental correlation, and shown that it is problematic for multimodal learning. However, have not yet proposed way to miligate it. We believe this is a promising direction for future work, since this improve the efficacy of multimodal learning in data-scarce settings. One example is to use our method in the acquisition step of active learning. We can collect data to reduce the KL divergence between the latent posterior and prior, which corresponds to collecting data that does not exhibit incidental correlation.
Acknowledgments
This work was supported by grants from the National Institutes of Health (P41EB017183), the National Science Foundation (HDR-1922658, CHE-2231174 DMS-2310831), the Gordon and Betty Moore Foundation (9683), Hyundai Motor Company (Uncertainty in Neural Sequence Modeling), Samsung Advanced Institute of Technology (Next Generation Deep Learning: From Pattern Recognition to Al), and the Office of Naval Research (N00014-23-1-2500)
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A Appendix
A.1 Derivations
The ELBO is
ply x, = log ply,
x, xxx'x x'z')dz
ply,2 z x, x')
= log x))
q( x, x,x',y)
ply X, x, 2))pz
2 _x v)
log
g(z x,)
logp(y x,x', z)] (x(( x)) p(z)).
= v)
A.2 Results from Kivva et al. (2022)
We adopt the following definition of identifiability from Kivva el al. (2022). Let f&P denole the pushforward measure of P by f. Let P be family of probability distributions on Tn and be a family of functions f 1. + R".
1. For (P,f) EX F we say that the prior P is identifiable (from f2P) to an affine transformation for any (P, E P x F such that = fiP' there exists an invertible affine map h R - Rm such that P' = hyP (i.e., P' is the pushforward measure of P by h).
2. For (P, PxF say that the pair () is idenlisiable (from J2P) up to an offine trunsformation if for any (P', E P x F such that f&P = f.P' there exists an invertible affine map h. : R - R
such that f h h- and P' = h.P.
ʃ is said to weakly injective if (i) there exists Ti IR" and 6 > s.t. [-- = for every e (rro 8) n (RR"), and (ii) {a E IR" (f-) xc) C [(R") has measure zero with respect the Lebesgue measure on (IR"). According to Kivva al. (2022), ReLU networks are generally weakly injective under simple assumptions their architecture.
Assuming that the prior over the latent variable Z is Gaussian mixture that factorizes over unobserved discrete variable U, and the decoder is piecewise affine and weakly injective, then P(U, 2) is identifiable from the observed data distribution P(X) up to an affine transformation of Z.
A.3 Implementation details
In our experiments, we trained for certain number of epochs M that depends on the size of the dataset N. Here are the values of M and N for the toy problem, as well as with VQA v2.0 and NIVR2.
Table 1: Toy problem
Table 2: VQA v2.0
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A.4 Additional experimental results
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Figure 9: Detecting incidental correlation the toy problem with D 16, b 1.5, and 0.1.
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Figure 10: Comparing multimodal and unimodal learning the toy problem with D 16, 6 1.5, and
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Figure 11: Detecting incidental correlation the toy problem with D = 1, b == 3, and 1.
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Figure 12: Comparing multimodal and unimodal learning on the toy problem with D = 1, = 3, and a 1.
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Figure 13: Detecting incidental correlation the toy problem with D 16, b 3, and o 1.
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Figure 14: Comparing multimodal and unimodal learning the toy problem with D =1,, b
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Figure 15: Detecting incidental correlation VQA v2.0 and NLVR2 with smaller model with latent dimension 128 and 32 components in the mixture prior.
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Reviews:
[{"review_id": "mI80IkGVka", "reviewer": "Reviewer_sw4q", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "*Strengths:*\n* The problem of understanding when multimodal models (or even unimodal models) make predictions based on spurious attributes of the data distribution is a very interesting and relevant direction.\n* The intuitive direction of trying to model possible confounding information using the latent space of a VAE is a promising direction.\n\n*Weaknesses:*\n* A central part of the experiments involves comparing what is called an identifiable VAE with a learnable mixture latent space and a so-called unidentifiable standard VAE, based on the theoretical results from Kivva et al. 2022. I am not an expert on identifiable VAEs but from my understanding of the claims in Kivva et al. 2022 Section 3.4 \"Classical VAE\" it appears that classical VAEs are considered identifiable and a special case of the mixture VAE. Why does the paper claim that the classical VAE is unidentifiable in the context of Kivva et al.? I am confused on this point and it is central to the experiment section.\n* The scope of the method and experiments seem very limited. The main method simply uses the KL divergence term of VAE learning to detect whether spurious correlations exist for small sample sizes. However, there is no heuristic presented for determining whether a sample size is sufficiently large to be free from spurious correlations. The method also does not include a constructive way of reducing spurious correlations when they are detected. Better practical applications would make the method more appealing.\n* It is not entirely clear that spurious correlations are the reason why KL divergence is high for low sample sizes. Could there be other aspects of small sample sizes that cause this?\n* The problem of small sample size learning in the context of multimodal models might be of limited interest. Investigating the method at scale would better display its potential.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the problem of detecting spurious correlations between different data modalities in the small sample size regime. The proposed method uses a conditional VAE model with a Gaussian mixture latent space of a response conditioned on two inputs with a latent variable that represents a possible unobserved variable influencing the inputs and response. The ground truth situation is that the response is conditionally independent of the unobserved latent variable given the inputs, but it can become conditionally dependent in the small sample regime. The proposed method uses the KL term of VAE learning to as a indicator of spurious correlations from low samples sizes. High KL is interpreted to mean that spurious correlations are being represented by z, and low KL is interpreted to mean that spurious correlation are not being learned because the encoder is not needed. Experiments on synthetic data and VQAv2 show that KL decreases with sample size.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* Please clarify why the vanilla VAE is presented as unidentifiable, especially with reference to Section 3.4 of Kivvas et al. 2022.\n* Is there a way to apply the method to large scale datasets which might not be balanced? For example, improving the balancing on VQA v1.", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "7Eb00VGbA0", "reviewer": "Reviewer_Ft39", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "- strengths\n    - the paper discusses important problem of \"model underutilization\" and discusses a new concept called \"incidental correlation\". \n    - the idea of using VAE to identify \"incidental correlation\" is interesting\n\n- weakness\n    - the writing of the paper has multiple unclear remarks, for examples\n        - it is unclear how \"incidental correlation\" is different from the well-known terms such as spurious correlation, confounding factors, or dataset bias etc\n        - the authors create multiple terms such as \"Multimodal generating process\" and \"Spurious generating process\", while it seems the authors suggest the these two terms are referring to two different scenarios mainly being differentiated by whether p(y|d(x)) equalize to p(y|x) or not, the names \"Multimodal\" and \"Spurious\" are not even orthogonal to each other. \n        - It's unclear why \"Small datasets that are sampled from the MGP, where u and y are conditionally independent given the inputs, can have higher likelihood under the SGP, where this independence does not hold\" This seems to be a key assumption used in the paper, while this is an often observed phenomenon in practices, it does not seem to hold when the authors put into their theoretical framework, if we are talking about uniform sampling. \n       - \"g(u) is a function that determines the amount of information that passes from u to y given the inputs\" not sure what does \"amount of information\" refers to. \n    - the synthetic experiments setting seems to limited\n       - will the synthetic results different if we test under more various settings of the parameters (1.5, 0.1)?\n       - if the data are uniformally sampled, aren't Figure 4(a) and Figure 4(b) have the same error rate while using single modality? then why a model will favor one in one case over the other one in the other? \n   - regarding real dataset experiment\n      - there are tons of datasets that are proven to have spurious features, e.g. [1]. Probably the authors can demonstrate the usage of their methods on more datasets with known spurious features, the results might be more convincing. \n      - it might be better to demonstrate accuracy-improving experiments on popular datasets. \n\n\n[1]. Select-Additive Learning: Improving Generalization in Multimodal Sentiment Analysis", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper addresses a key problem in multimodal learning known as \"modality underutilization,\" where multimodal neural networks fail to utilize all modalities, leading to weaker generalization or biased predictions. The authors introduce a concept called \"incidental correlation,\" that leads to modality underutilization. The authors further propose a method to detect incidental correlation through latent variable modeling. They specify an identifiable variational autoencoder (VAE), allowing them to interpret the Kullback-Leibler divergence between the latent posterior and prior as the severity of incidental correlation. The paper conducts experiments with synthetic data and the VQA v2.0 dataset, validating the authors' theory of incidental correlation and demonstrating its effect on modality underutilization.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please address to the weakness listed above. ", "broader_impact_concerns": "none noted", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "vJWmGzhrDx", "reviewer": "Reviewer_csjL", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths:\n* The paper is super well written and I understand fully and approve of (most of) what's been done, the definition of incidental correlation and why this may hurt performance, and the broader context in which this paper may be important or limited (e.g. the case of Fig 2b). \n* The experiments carefully validated their hypotheses and results are consistent across datasets and problems. \n* Their method is practical and can be easily used for many problems. \n\n## Weaknesses\n* I understand the authors want to \\emph{detect} incidental correlations, but do not further provide a method for improve methods that were affected by it. This is a tiny bit disappointing (although the authors are aware of it based on Conclusions). \n* I feel that, although it is possible that a more complicated model (with an arrow from $u$ to $z$) can become a winning model in small-data regime, there isn't any explanation or illustration how this dependence could be. This is more out of curiosity, but helps strenghtens the authors' hypotheses.\n* There is a problem with the CVAE setup: the prior does not depend on the conditioning variables.\n* The distinction between the indentifiable and unidentifiable CVAEs need more explanation. The cited paper of Kivva (2022) is quite dense, so the authors should explain briefly why choosing a single, fixed prior makes the CVAE unidentifiable, or just state the assumption needed for identifiability.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Based on the observation that multimodal learning usually do not generalise better than unimodal learning, the authors hypthesizes that this is because small dataset creates the possibility of suprious correlations between an unobserved confounder in small-data regime. The authors proposed a method for detecting this \\emph{incidental correlation} and showed the plausibility of their hypothesis and effectiveness of their method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "## Critical:\n1. Please justify the use of an independent prior in the CVAE setup. Logically, u and y are conditionally independent given x and x', this implies that KL[q(z|x, x', y)||p(z|x, x')] =0, not KL[q(z|x, x', y)||p(z|)] =0. This is quite important to explain, or run experiments to justify which one is better empirically. \n1. Please address this question regarding Section 4: is it the case that (at least theoretically) posterior collapse is not possible when the model is identifiable? And is it the case that the method of Kivva et al (2022) can always achieve identifiability? If so, under what conditions? Because if this is the case, then we can have conditions that the identifiable model can avoid posterior collapse under those conditions. This is conceptually an important chain of reasoning. \n1.  Section 5.2.1. A Gaussian mixture with 128 components is quite large, and the dimensionality of the z-space is also huge. Can the authors run some experiments with lower dimensions? Or is it not important? This helps practitioners know what kind of dimensionalities they should expect to run to detect incidental correlations. \n\n## Suggestions\nI have a few suggestions that may help reader understand the paper better\n1. typo: page 2, 2nd last para. line 4: \"edge makes which makes\"\n2. Writing: in Section 5, it would help if the authors could allude to the readers that there will be a few experiments with different techniques (with u observed and unobserved, and comparing multipmodal vs unimodal learning). Even better, let us know what you are running these different comparisons that serve very similar purposes.\n3. typo: Sec. 5.1.2, last para, first line: \"show that the for the \"\n4. second to last line of page 8: if I understand correctly, it should be the log-probability of the \"true\" target, right? It doesn't hurt to clarify a bit more.\n5. All figures: what are the errorbars? Are there any reasons not to run statistical tests on claims like \"... is large when datasize is small\"? Could we do some t-test on comparison with zero, or on the slope of the lines? \n", "broader_impact_concerns": "Don't think there is any substantial concerns. ", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "4wXaPScxOb", "reviewer": "Reviewer_ARpp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Pros:\n1. The paper is written clearly and the motivations are clearly stated.\n2. The method is concise and easy to plug in. From the description in the paper, the work could generalize to a variety of application domains.\n3. One detailed toy example is provided to explain how the proposed method works and it's further validated on a real-world datasets VQA 2.0.\n\nCons:\n1. Besides detecting whether incidental correlation is present or not, to determine the need for more data, I think another direction would be more interesting: if the dataset is large enough to get rid of the the incidental correlation issue. Furthermore, if this work can propose the potential directions of which data to further collect.\n2. Small datasets are more likely to suffer from incidental correlation issue. While an unobserved var $u$ is a possibility, I would intuitively more suspect another scenario: small amount of samples are not enough to depict the data distribution, so it's not another DGP is more likely to be learnt, but instead one was \"randomly\" selected from multiple \"eligible\" DGPs. Also, I think it's a bit hard to determine if adding $u$ is enough to narrow down the DGP candidates to the ground-truth one?\n3. Close-to-zero KL divergence is also often known as \"over-regularization\" (or posterior collapse as you mentioned). Though Gaussian mixture is proposed to alleviate the issue, how do you pre-define or learn these Gaussians? Are they learnt and defined case-by-case as in the toy example?\n4. Eq. (3) has a typo in $q(z|x,x',z)$. Pls correct.\n5. While I generally agree all modalities should be used if necessary, I wonder if there are some cases fewer modalities can make accurate predictions and forcing the model to use all modalities hurt the performance on the contrary?\n6. You mentioned multiple modalities like text, vision, speech, etc. in the introduction. Given that you place your work as a detection method, I think it's better to test the method on more datasets.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this work, it raises a concern that not all modalities are used to boost more accurate predictions in the multimodal learning. Though the existing works address the issue by ensuring no systematic biases in the data creation or enlarging the neural network's capacity, the authors point out that such *modality underutilization* could still occur in the small data regime. They proposed an assumption that instead of the ground-truth underlying data generating process, it's more likely a different *spurious* data generating process is learnt. The authors propose an identifiable variational autoencoder, which conditions on the multimodal observations $x, x'$ and further uses target $y$ to learn the posterior for a latent variable $z$ (encoder). The decoder reads $x, x', z$ to predict the target $y$. The KL divergence between the learnt posterior and the Gaussian mixture prior is defined as the severity of incidental correlation. A toy problem with synthetic data is illustrated to demonstrate the proposed method. The identifiable VAE is also further validated on a real-world dataset VQA 2.0.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. I think the Gaussian mixture is a critical module in this work. Pls elaborate on how you define or learn the Gaussian mixture. Is it dataset-dependent?\n2. It would be more convincing if you can test your method on more real-world datasets or incorporating more modalities to demonstrate its generalizability.\n3. For latent variable modeling and disentangled representation learning related works, I would suggest adding [1,2] into the discussion.\n\n[1] Li, Y. and Mandt, S., 2018, July. Disentangled sequential autoencoder. In International Conference on Machine Learning (pp. 5670-5679). PMLR.\n\n[2] Bai, J., Wang, W. and Gomes, C.P., 2021. Contrastively disentangled sequential variational autoencoder. Advances in Neural Information Processing Systems, 34, pp.10105-10118.", "broader_impact_concerns": "The Broader Impact Statement section is not presented, and I don't think it is applicable to this paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: All reviewers thought (1) the submission is well written, and (2) the problem studied here is important. Most reviewers did not engage in the discussion, unfortunately.

Two reviewers remained unconvinced after reading the authors' responses. Two sticking points were:

(i) *The experiments could be expanded to include more real-world datasets*: a new dataset was added in the latest revision. The synthetic data were designed to study the problem in the limited data regime, so I don't think this is an issue given the scope of the claims.

(ii) *Whether the KL divergence between the posterior and prior is an appropriate metric to measure spurious correlation*: additional discussion has been added and experimental results have shown the utility of this metric.

All other requested changes have been incorporated and discussed. I recommend acceptance.
Decision: Accept (poster)