4 Matrix and Tensor Factorization Methods …
65
w
(t)
d,k ∼ h t,k N
0,
α
(t)
d,k
−1
+
1 − h t,k
δ 0
h t,k ∼ Bernoulli(π k )
π k ∼ Beta(a
π
, b
π
)
α
(t)
d,k ∼ Gamma(a
α
, b
α
)
τ
(t)
∼ Gamma(a
τ
, b
τ
).
Here, the latent variables Z and U are common to all the tensors and capture the
underlying patterns, while W
(t) translate these patterns for each tensor. The binary
variables h t,k control the view activity through a spike and slab prior and are automatically learned from the data. The model also enforces feature-wise sparsity through α
to learn sparse features that are easier to interpret. The method is implemented using a
Gibbs sampler in R programming language and made available freely (http://research.
ics.aalto.fi/mi/software/MTF). The implementation learns the model parameters in a
Bayesian formulation, while providing default settings for all the hyperparameters.
4.3 Selected Case Studies
4.3.1 Toxicogenomic Data Sets
The toxicogenomic tools described in this chapter are primarily built upon the Connectivity Map (CMap) and NCI60 data sets. CMap, introduced by the US Broad
Institute, is a compendium of gene expression response profiles from 1309 small
molecules comprising mostly FDA approved drugs ([46]; https://www.broadinstitute.
org/connectivity-map-cmap). The post-treatment measurements originated from
three main cancer cell lines spanning different tissues or cell types, namely, breast
(MCF7), prostate (PC3), and blood (HL60). CMap has been widely used to study
interactions between small molecules, genes, and diseases for various purposes
including understanding the drug MoA, identifying biologically similar compounds
as well as molecular mechanisms of toxicity. The treatment versus control differential gene expression (log2 readout) was obtained from the CMap data set, such
that positive expression values represent up-regulation and negative represent downregulation as a result of treatment [4].
The NCI60 is a unique data repository from the US National Cancer Institute (NCI)
that screened thousands of compounds over 59 cancer cell lines to provide measurements of drug responses (Shoemaker 2006; https://dtp.cancer.gov/discovery_
development/nci-60). Drug response metrics include GI50 (50% Growth Inhibition),
total growth inhibition (TGI), and LC50 (50% Lethal Concentration). A large number
65
w
(t)
d,k ∼ h t,k N
0,
α
(t)
d,k
−1
+
1 − h t,k
δ 0
h t,k ∼ Bernoulli(π k )
π k ∼ Beta(a
π
, b
π
)
α
(t)
d,k ∼ Gamma(a
α
, b
α
)
τ
(t)
∼ Gamma(a
τ
, b
τ
).
Here, the latent variables Z and U are common to all the tensors and capture the
underlying patterns, while W
(t) translate these patterns for each tensor. The binary
variables h t,k control the view activity through a spike and slab prior and are automatically learned from the data. The model also enforces feature-wise sparsity through α
to learn sparse features that are easier to interpret. The method is implemented using a
Gibbs sampler in R programming language and made available freely (http://research.
ics.aalto.fi/mi/software/MTF). The implementation learns the model parameters in a
Bayesian formulation, while providing default settings for all the hyperparameters.
4.3 Selected Case Studies
4.3.1 Toxicogenomic Data Sets
The toxicogenomic tools described in this chapter are primarily built upon the Connectivity Map (CMap) and NCI60 data sets. CMap, introduced by the US Broad
Institute, is a compendium of gene expression response profiles from 1309 small
molecules comprising mostly FDA approved drugs ([46]; https://www.broadinstitute.
org/connectivity-map-cmap). The post-treatment measurements originated from
three main cancer cell lines spanning different tissues or cell types, namely, breast
(MCF7), prostate (PC3), and blood (HL60). CMap has been widely used to study
interactions between small molecules, genes, and diseases for various purposes
including understanding the drug MoA, identifying biologically similar compounds
as well as molecular mechanisms of toxicity. The treatment versus control differential gene expression (log2 readout) was obtained from the CMap data set, such
that positive expression values represent up-regulation and negative represent downregulation as a result of treatment [4].
The NCI60 is a unique data repository from the US National Cancer Institute (NCI)
that screened thousands of compounds over 59 cancer cell lines to provide measurements of drug responses (Shoemaker 2006; https://dtp.cancer.gov/discovery_
development/nci-60). Drug response metrics include GI50 (50% Growth Inhibition),
total growth inhibition (TGI), and LC50 (50% Lethal Concentration). A large number