The document discusses using xgboost for machine learning and summarizes steps to prepare data for xgboost models. It recommends binding feature data together and writing it out in the libsvm format for efficient reading into an xgboost DMatrix object. It also suggests using the data.table package to write out libsvm files in parallel for improved performance on large datasets.
Introduction of “Fairness in Learning: Classic and Contextual Bandits”Kazuto Fukuchi
1. The document discusses fairness constraints in contextual bandit problems and classic bandit problems.
2. It shows that for classic bandits, Θ(k^3) rounds are necessary and sufficient to achieve a non-trivial regret under fairness constraints.
3. For contextual bandits, it establishes a tight relationship between achieving fairness and Knows What it Knows (KWIK) learning, where KWIK learnability implies the existence of fair learning algorithms.
Conditional Image Generation with PixelCNN Decoderssuga93
The document summarizes research on conditional image generation using PixelCNN decoders. It discusses how PixelCNNs sequentially predict pixel values rather than the whole image at once. Previous work used PixelRNNs, but these were slow to train. The proposed approach uses a Gated PixelCNN that removes blind spots in the receptive field by combining horizontal and vertical feature maps. It also conditions PixelCNN layers on class labels or embeddings to generate conditional images. Experimental results show the Gated PixelCNN outperforms PixelCNN and achieves performance close to PixelRNN on CIFAR-10 and ImageNet, while training faster. It can also generate portraits conditioned on embeddings of people.
Interaction Networks for Learning about Objects, Relations and PhysicsKen Kuroki
For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide.
https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics
Introduction of "TrailBlazer" algorithmKatsuki Ohto
論文「Blazing the trails before beating the path: Sample-efficient Monte-Carlo planning」紹介スライドです。NIPS2016読み会@PFN(2017/1/19) https://connpass.com/event/47580/ にて。
Fast and Probvably Seedings for k-MeansKimikazu Kato
The document proposes a new MCMC-based algorithm for initializing centroids in k-means clustering that does not assume a specific distribution of the input data, unlike previous work. It uses rejection sampling to emulate the distribution and select initial centroids that are widely scattered. The algorithm is proven mathematically to converge. Experimental results on synthetic and real-world datasets show it performs well with a good trade-off of accuracy and speed compared to existing techniques.
InfoGAN: Interpretable Representation Learning by Information Maximizing Gen...Shuhei Yoshida
Unsupervised learning of disentangled representations was the goal. The approach was to use GANs and maximize the mutual information between generated images and input codes. This led to the benefit of obtaining interpretable representations without supervision and at substantial additional costs.
Improving Variational Inference with Inverse Autoregressive FlowTatsuya Shirakawa
This slide was created for NIPS 2016 study meetup.
IAF and other related researches are briefly explained.
paper:
Diederik P. Kingma et al., "Improving Variational Inference with Inverse Autoregressive Flow", 2016
https://papers.nips.cc/paper/6581-improving-variational-autoencoders-with-inverse-autoregressive-flow
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness and well-being.
3. 円の場合
circ.lua
x = sin θ for t = 0, 59, 1 do
th = math.pi / 2 * t / 59
y = cos θ x, y = math.sin(th), math.cos(th)
π t
θ = (0 ≤ t < 60) print(x, y)
end
2 59
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
図 1: 円
3 / 20
4. 円錐曲線の極座標一般系
x = r sin θ
y = r cos θ + e
1 − e2
r =
1 + e cos θ
e = 0 の場合、円
0 < e < 1 の場合、楕円
e = 1 の場合、放物線(r の分子は定数とする)
1 < e の場合、双曲線
4 / 20
5. 双曲線の曲座標表示
bola.lua
e, div = 2, 240
x = r sin θ for t = 0, div, 1 do
y = r cos θ + e th = 2 * math.pi * t / div
r = (1-e*e)/(1+e*math.cos(th))
1 − e2 x, y = r*math.sin(th), r*math.cos(th)+e
r = print(x, y)
1 + e cos θ end
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 0 2 4 6 8 10
図 2: 双曲線(全体)
5 / 20
6. 右肩下がりの双曲線
円の場合と同じように、(0,1) から出発して右肩下がりに
図 2 の右下の部分のみを使いたい
下の双曲線の頂点を (0,1) に移動する
y に 2 を足す
t = 0 の時に θ = π となるように
t が増えるに従い、θ は減らす
この時に、x 切片(y = 0)の時の θ を求める
1 − e2
cos θ + e + 2 = 0
1 + e cos θ
(1 − e 2 ) cos θ = −(e + 2)(1 + e cos θ)
e +2
cos θ = −
2e + 1
e +2
θ = arccos (− )
2e + 1
6 / 20
7. 右肩下がりの双曲線
bola.lua
e, div = 2, 59
d = math.pi - math.acos(-(e+2)/((2*e)+1))
for t = 0, div, 1 do
th = math.pi-(d*t/div)
r = (1-e*e)/(1+e*math.cos(th))
x, y = r*math.sin(th), r*math.cos(th)+e+2
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5 3
図 3: 双曲線(右肩下がり)
7 / 20
8. 切片を調節した双曲線
切片の x 座標を a にしたい
e+2
切片なので、この時の θ は arccos (− 2e+1 )
1 − e2
sin θ = a
1 + e cos θ
√ ( )
1 − e2 e +2 2
1− = a
1 − e 2e+1
e+2 2e + 1
√
3(e 2 − 1)
(2e + 1) = a
2e + 1
√
a2
e = +1
3
8 / 20
9. 切片を調節した双曲線
bola.lua
a, div = 0.8, 59
e = math.sqrt((a*a/3)+1)
d = math.pi - math.acos(-(e+2)/((2*e)+1))
for t = 0, div, 1 do
th = math.pi-(d*t/div)
r = (1-e*e)/(1+e*math.cos(th))
x, y = r*math.sin(th), r*math.cos(th)+e+2
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
図 4: 双曲線 9 / 20
10. 放物線の曲座標表示
para.lua
c, div = 1, 240
x = r sin θ for t = 0, div, 1 do
th = 2 * math.pi * t / div
y = r cos θ + 1 r = c/(1+math.cos(th))
c x, y = r*math.sin(th), r*math.cos(th)+1
r =
1 + cos θ print(x, y)
end
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-5 -4 -3 -2 -1 0 1 2 3 4 5
図 5: 放物線(全体)
10 / 20
11. 右肩下がりの放物線
円の場合と同じように、(0,1) から出発して右肩下がりに
図 5 の右の部分のみを使いたい
放物線の頂点を (0,1) に移動する
y から c を引く
2
t = 0 の時に θ = 0
t が増えるに従い、θ は増やす
この時に、x 切片(y = 0)の時の θ を求める
c c
cos θ + 1 − = 0
1 + cos θ 2
2−c
c cos θ = − (1 + cos θ)
2
(c + 2) cos θ = −(2 − c)
c −2
θ = arccos ( )
c +2
11 / 20
12. 右肩下がりの放物線
para.lua
c, div = 1, 59
b = math.acos((c-2)/(c+2))
for t = 0, div, 1 do
th = b*t/div
r = c/(1+math.cos(th))
x, y = r*math.sin(th), r*math.cos(th)+1-(c/2)
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
図 6: 放物線(右肩下がり)
12 / 20
13. 切片を調節した放物線
切片の x 座標を a にしたい
切片なので、この時の θ は arccos ( c−2 )
c+2
c
sin θ = a
1 + cos θ
√ ( )
c c −2 2
1− = a
1 + c−2
c+2
c +2
√
c + 2 8c
= a
2 c +2
a2
c =
2
13 / 20
14. 切片を調整した放物線
para.lua
a, div = 0.8, 59
c = a*a/2
b = math.acos((c-2)/(c+2)) for t = 0, div, 1 do
th = b*t/div
r = c/(1+math.cos(th))
x, y = r*math.sin(th), r*math.cos(th)+1-(c/2)
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
図 7: 放物線
14 / 20
15. 楕円の曲座標表示
elli.lua
e, div = 0.5, 240
x = r sin θ for t = 0, div, 1 do
y = r cos θ + e th = 2 * math.pi * t / div
r = (1-(e*e))/(1+(e*math.cos(th)))
1 − e2 x, y = r*math.sin(th), r*math.cos(th)+e
r = print(x, y)
1 + e cos θ end
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
図 8: 楕円(全体)
15 / 20
16. 右肩下がりの楕円
円の場合と同じように、(0,1) から出発して右肩下がりに
図 8 の右上の部分のみを使いたい
x 切片(y = 0)の時の θ を求める
1 − e2
cos θ + e = 0
1 + e cos θ
(1 − e 2 ) cos θ = −e(1 + e cos θ)
cosθ = −e
θ = arccos (−e)
16 / 20
17. 右肩下がりの楕円
elli.lua
e, div = 0.5, 59
b = math.acos(-e)
for t = 0, div, 1 do
th = b*t/div
r = (1-(e*e))/(1+(e*math.cos(th)))
x, y = r*math.sin(th), r*math.cos(th)+e
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
図 9: 楕円(右肩下がり)
17 / 20
18. 切片を調節した楕円
切片の x 座標を a にしたい
切片なので、この時の θ は arccos (−e)
1 − e2
sin θ = a
1 + e cos θ
1 − e2 √
1 − e2 = a
1 − e2
√
1 − e2 = a
√
e = 1 − a2
18 / 20
19. 切片を調整した楕円
elli.lua
a, div = 0.8, 59
c = math.sqrt(1-(a*a))
b = math.acos(-e)
for t = 0, div, 1 do
th = b*t/div
r = (1-(e*e))/(1+(e*math.cos(th)))
x, y = r*math.sin(th), r*math.cos(th)+e
print(x, y)
end
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
図 10: 楕円 19 / 20