Weakly supervised (WS), multiple instance (MI) data lives in numerous
interesting applications such as drug discovery, object detection, and
tumor prediction on whole slide images. The mildsvm package provides
an easy way to learn from this data by training Support Vector Machine
(SVM)-based classifiers. It also contains helpful functions for building
and printing multiple instance data frames.
The mildsvm package implements methods that cover a variety of data
types, including:
- ordinal and binary labels
- weakly supervised and traditional supervised structures
- vector-based and distributional-instance rows of data
A full table of functions with references is available below. We highlight two methods based on recent research:
omisvm()runs a novel OMI-SVM approach for ordinal, multiple instance (weakly supervised) data using the work of Kent and Yu (2022+)mismm()run the MISMM approach for binary, weakly supervised data where the instances can be thought of as a matrix of draws from a distribution. This non-convex SVM approach is formalized and applied to breast cancer diagnosis based on morphological features of the tumor microenvironment in Kent and Yu (2022).
A typical MI data frame (a mi_df) with ordinal labels might look like
this, with multiple rows of information for each of the bag_names
involved and a label that matches each bag:
library(mildsvm)
data("ordmvnorm")
print(ordmvnorm)
#> # An MI data frame: 1,000 × 7 with 200 bags
#> # and instance labels: 1, 1, 2, 1, 1, ...
#> bag_label bag_name V1 V2 V3 V4 V5
#> * <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 2 1 1.55 -0.977 1.33 -0.659 -0.694
#> 2 2 1 0.980 -2.10 -0.618 2.15 -0.718
#> 3 2 1 6.16 -0.275 2.07 -0.624 0.444
#> 4 2 1 2.90 -2.15 -0.0407 -0.0629 1.38
#> 5 2 1 2.62 -1.70 1.35 -1.66 1.23
#> 6 4 2 3.39 -0.927 1.95 0.216 -0.164
#> 7 4 2 3.05 -0.930 1.34 -0.457 0.362
#> 8 4 2 6.63 -4.57 4.66 -0.00729 1.03
#> 9 4 2 4.38 -0.714 2.32 0.0996 0.379
#> 10 4 2 2.43 -4.28 1.08 0.283 -1.14
#> # … with 990 more rows
# dplyr::distinct(ordmvnorm, bag_label, bag_name)The mildsvm package uses the familiar formula and predict methods that
R uses will be familiar with. To indicate that MI data is involved, we
specify the unique bag label and bag name with
mi(bag_label, bag_name) ~ predictors:
fit <- omisvm(mi(bag_label, bag_name) ~ V1 + V2 + V3,
data = ordmvnorm,
weights = NULL)
print(fit)
#> An misvm object called with omisvm.formula
#>
#> Parameters:
#> method: qp-heuristic
#> kernel: linear
#> cost: 1
#> h: 1
#> s: 4
#> scale: TRUE
#> weights: FALSE
#>
#> Model info:
#> Levels of `y`: chr [1:5] "1" "2" "3" "4" "5"
#> Features: chr [1:3] "V1" "V2" "V3"
#> Number of iterations: 4
predict(fit, new_data = ordmvnorm)
#> # A tibble: 1,000 × 1
#> .pred_class
#> <fct>
#> 1 2
#> 2 2
#> 3 2
#> 4 2
#> 5 2
#> 6 4
#> 7 4
#> 8 4
#> 9 4
#> 10 4
#> # … with 990 more rowsOr, if the data frame has the mi_df class, we can directly pass it to
the function and all features will be included:
fit2 <- omisvm(ordmvnorm)
#> Warning: Weights are not currently implemented for `omisvm()` when `kernel ==
#> 'linear'`.
print(fit2)
#> An misvm object called with omisvm.mi_df
#>
#> Parameters:
#> method: qp-heuristic
#> kernel: linear
#> cost: 1
#> h: 1
#> s: 4
#> scale: TRUE
#> weights: FALSE
#>
#> Model info:
#> Levels of `y`: chr [1:5] "1" "2" "3" "4" "5"
#> Features: chr [1:5] "V1" "V2" "V3" "V4" "V5"
#> Number of iterations: 3You can install the released version of mildsvm from CRAN with:
install.packages("mildsvm")Alternatively, you can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("skent259/mildsvm")mildsvm also works well MI data with distributional instances. There
is a 3-level structure with bags, instances, and samples. As in
MIL, instances are contained within bags (where we only observe the
bag label). However, for MILD, each instance represents a distribution,
and the samples are drawn from this distribution.
You can generate MILD data with generate_mild_df():
# Normal(mean=0, sd=1) vs Normal(mean=3, sd=1)
set.seed(4)
mild_df <- generate_mild_df(
ncov = 1, nimp_pos = 1, nimp_neg = 1,
positive_dist = "mvnormal", positive_mean = 3,
negative_dist = "mvnormal", negative_mean = 0,
nbag = 4,
ninst = 2,
nsample = 2
)
print(mild_df)
#> # An MILD data frame: 16 × 4 with 4 bags, 8 instances
#> # and instance labels: 0, 0, 0, 0, 0, ...
#> bag_label bag_name instance_name X1
#> <dbl> <chr> <chr> <dbl>
#> 1 0 bag1 bag1inst1 1.51
#> 2 0 bag1 bag1inst1 -0.463
#> 3 0 bag1 bag1inst2 1.79
#> 4 0 bag1 bag1inst2 1.67
#> 5 0 bag2 bag2inst1 0.299
#> 6 0 bag2 bag2inst1 0.666
#> 7 0 bag2 bag2inst2 0.0118
#> 8 0 bag2 bag2inst2 0.146
#> 9 1 bag3 bag3inst1 0.546
#> 10 1 bag3 bag3inst1 0.473
#> 11 1 bag3 bag3inst2 1.94
#> 12 1 bag3 bag3inst2 1.25
#> 13 1 bag4 bag4inst1 1.11
#> 14 1 bag4 bag4inst1 0.768
#> 15 1 bag4 bag4inst2 0.111
#> 16 1 bag4 bag4inst2 -0.290You can train a MISVM classifier using mismm() on the MILD data with
the mild() formula specification:
fit3 <- mismm(mild(bag_label, bag_name, instance_name) ~ X1, data = mild_df, cost = 100)
# summarize predictions at the bag layer
library(dplyr)
mild_df %>%
dplyr::bind_cols(predict(fit3, mild_df, type = "raw")) %>%
dplyr::bind_cols(predict(fit3, mild_df, type = "class")) %>%
dplyr::distinct(bag_label, bag_name, .pred, .pred_class)
#> # A tibble: 4 × 4
#> bag_label bag_name .pred .pred_class
#> <dbl> <chr> <dbl> <fct>
#> 1 0 bag1 -1.18 0
#> 2 0 bag2 0.482 1
#> 3 1 bag3 1.00 1
#> 4 1 bag4 1.00 1If you summarize a MILD data set (for example, by taking the mean of
each covariate), you can recover a MIL data set. Use
summarize_samples() for this:
mil_df <- summarize_samples(mild_df, .fns = list(mean = mean))
print(mil_df)
#> # A tibble: 8 × 4
#> bag_label bag_name instance_name mean
#> <dbl> <chr> <chr> <dbl>
#> 1 0 bag1 bag1inst1 0.522
#> 2 0 bag1 bag1inst2 1.73
#> 3 0 bag2 bag2inst1 0.483
#> 4 0 bag2 bag2inst2 0.0791
#> 5 1 bag3 bag3inst1 0.510
#> 6 1 bag3 bag3inst2 1.59
#> 7 1 bag4 bag4inst1 0.941
#> 8 1 bag4 bag4inst2 -0.0896You can train an MI-SVM classifier using misvm() on MIL data with the
helper function mi():
fit4 <- misvm(mi(bag_label, bag_name) ~ mean, data = mil_df, cost = 100)
print(fit4)
#> An misvm object called with misvm.formula
#>
#> Parameters:
#> method: heuristic
#> kernel: linear
#> cost: 100
#> scale: TRUE
#> weights: ('0' = 0.5, '1' = 1)
#>
#> Model info:
#> Features: chr "mean"
#> Number of iterations: 2| Function | Method | Outcome/label | Data type | Extra libraries | Reference |
|---|---|---|---|---|---|
omisvm() |
"qp-heuristic" |
ordinal | MI | gurobi | [1] |
mismm() |
"heuristic" |
binary | distributional MI | — | [2] |
mismm() |
"mip" |
binary | distributional MI | gurobi | [2] |
mismm() |
"qp-heuristic" |
binary | distributional MI | gurobi | [2] |
misvm() |
"heuristic" |
binary | MI | — | [3] |
misvm() |
"mip" |
binary | MI | gurobi | [3], [2] |
misvm() |
"qp-heuristic" |
binary | MI | gurobi | [3] |
mior() |
"qp-heuristic" |
ordinal | MI | gurobi | [4] |
misvm_orova() |
"heuristic" |
ordinal | MI | — | [3], [1] |
misvm_orova() |
"mip" |
ordinal | MI | gurobi | [3], [1] |
misvm_orova() |
"qp-heuristic" |
ordinal | MI | gurobi | [3], [1] |
svor_exc() |
"smo" |
ordinal | vector | — | [5] |
smm() |
— | binary | distributional vector | — | [6] |
- MI: multiple instance
- SVM: support vector machine
- SMM: support measure machine
- OR: ordinal regression
- OVA: one-vs-all
- MIP: mixed integer programming
- QP: quadratic programming
- SVOR: support vector ordinal regression
- EXC: explicit constraints
- SMO: sequential minimal optimization
[1] Kent, S., & Yu, M. (2022+). Ordinal multiple instance support vector machines. In prep.
[2] Kent, S., & Yu, M. (2022). Non-convex SVM for cancer diagnosis based on morphologic features of tumor microenvironment. arXiv preprint arXiv:2206.14704.
[3] Andrews, S., Tsochantaridis, I., & Hofmann, T. (2002). Support vector machines for multiple-instance learning. Advances in neural information processing systems, 15.
[4] Xiao, Y., Liu, B., & Hao, Z. (2017). Multiple-instance ordinal regression. IEEE Transactions on Neural Networks and Learning Systems, 29(9), 4398-4413.
[5] Chu, W., & Keerthi, S. S. (2007). Support vector ordinal regression. Neural computation, 19(3), 792-815.
[6] Muandet, K., Fukumizu, K., Dinuzzo, F., & Schölkopf, B. (2012). Learning from distributions via support measure machines. Advances in neural information processing systems, 25.