tensorFM: Low-Rank Approximations of Cross-Order Feature Interactions
Authors: Alessio Mazzetto, Mohammad Mahdi Khalili, Laura Fee Nern, Michael Viderman, Alex Shtoff, Krzysztof Dembczyński
Organizations: Brown University · Department of Computer Science Brown University Providence, RI, United States · Ohio State University · Yahoo Research · CSE Department Ohio State University Columbus, OH, United States · Yahoo Research, United States · Yahoo Research, Germany · Yahoo Research, Ireland · Technology Innovation Institute · Technology Innovation Institute, Israel · Poznan University of Technology · Institute of Computing Sciences Poznan University of Technology, Poznan, Poland
We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical values as features. Such problems frequently arise in practical applications, including click-through rate prediction and social sciences. We introduce and analyze {tensorFM}, a new model that efficiently captures high-order interactions between attributes via a low-rank tensor approximation representing the strength of these interactions. Our model generalizes field-weighted factorization machines. Empirically, tensorFM demonstrates competitive performance with state-of-the-art methods. Additionally, its low latency makes it well-suited for time-sensitive applications, such as online advertising.
Figures & tables
Recidivism
Age
Gender
Charge
Re-arrest
-1
24
M
Felony
0
-1
34
F
Felony
0
1
19
M
Misd.
1
1
25
F
Felony
0
Table 1: Examples of multi-field categorical data: recidivism (left) and online advertising (right).
Model
Avazu
Criteo
Test Log-Loss
Test AUC
Test Log-Loss
Test AUC
LR
0.3873
76.53
0.4551
79.39
FM
0.3810
77.69
0.4470
80.44
FwFM
0.3805
77.28
0.4428
80.87
AFM
0.3833
77.31
0.4462
79.75
CN
0.3841
77.16
0.4514
79.55
Table 2: Comparison of baseline performance in terms of the test set AUC (%) and LogLoss. The best results are bold and the second best results are underlined .
Table 3
Model
3-wise Interactions
4-wise Interactions
Test Log-Loss
Test AUC
Test Log-Loss
Test AUC
LR
0.6896
54.87
0.6917
53.18
FM
0.6508
66.07
0.6738
61.11
FwFM
0.6514
65.99
0.6734
61.07
AFM
0.6218
71.96
0.6730
61.56
CN
0.6676
61.73
0.6813
57.70
Table 5: Comparison of baseline performance in terms of the test set AUC and LogLoss ( % ) over the synthetic data for 3-wise and 4-wise interactions. The best results are bold and the second best results are underlined .
Model
3-wise Interactions
4-wise Interactions
Test Log-Loss
Test AUC
Test Log-Loss
Test AUC
LR
0.6912
53.59
0.6896
54.87
FM
0.6869
58.01
0.6883
55.83
FwFM
0.6572
64.99
0.6771
60.18
AFM
0.6912
53.59
0.6914
53.36
CN
0.6834
57.76
0.6867
56.04
Table 6: Comparison of baseline performance in terms of the test set AUC (%) and LogLoss over the synthetic data containing 100 columns, for 3-wise and 4-wise interactions. The best results are bold and the second best results are underlined .
Figure 6Figure 7
Model
Time (ms)
TensorFM(1,2)
0.00115
TensorFM(2,2)
0.00152
TensorFM(4,2)
0.00286
TensorFM(1,3)
0.00194
TensorFM(2,3)
0.00367
TensorFM(4,3)
0.00703
Table 7: Inference complexity (right) and empirical inference time in milliseconds (left) of different models. The empirical inference complexity is evaluated as the average inference time on 100000 synthetic data points with n=100 fields and embedding size k=8 .
Figure 5: Heatmap of the 36 strongest learned third-order interaction strengths aggregated across field triplets.