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❅ ✙ ★✰✾❇❆☞❈❉✮❊❀❋❀❍●❏■❑❃✰✮☎▲✤●❉✦✩✪◆▼❖✴P✦✩◗✫❈❏✾❄❘❚❙ ❯✵❱❳❲ ✾✑▲❩❨❬●❭✪✫❪✫❫☎▲✑❴❵❃❄❈❉✮❊❀❋❀❛❈❉✮✫◗❄✾❄❈❝❜❞❪❂✮❄●❭✴☛❀❡✱❢✴✷✦✩❘ ❫✫✪✫❣❂✪✰✦❊❤✐✪❥✱❦❫✫✪✰❃✑▲✤●❉✦✩✪ ❧♠❱✛♥ ●♦✪✰✶♣▲q★✰✾♣❫✫✪✫❣❂✪✰✦❊❤r✪✘✱❢❫✫✪✰❃❍▲✤●❉✦✩✪ s♠❱t❱✉❱✔❱ ▲❋✦✈❘✇●♦✪❄●❭❘✇●②①☎✾✓✾❄✴③✴P✦✵✴☛❀r✦✩✪✇✱❢❫☎▲q❫✫✴P✾❚●❭✪✫❪✫❫☎▲❬❀ �✂✁☎✄✝✆✟✞✡✠☛✆☞✄✍✌✎�✂✁✑✏☞✒✓✠✔✆✡✞✡✠✖✕✘✗ ✚✛✏✜✕✢✁✤✣ ✥✧✦✩★✫✪✭✬✩✮✫✪✰✯✲✱✳✦✵✴✷✶ ✸✺✹✼✻ ✽✿✾✑❀❁✾✧✮❂✴✷❃❄★

Learned Function (Classifier) snow guess 1 guess 2 guess 3 Precipitation rain 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Temperature Unknown Function Samples snow Precipitation rain 0 0.2 0.4 0.6 0.8 1 Temperature Training Sample

❱ ❱ ✬ ● ● ✁ ❴ ❴ ❀ ❱ ✏ ✾✰✮ ✴✺✪❄●♦✪✰✯ ▼❖✴P✾☎✶ ●❉❃❍▲ ●❝✦✩✪❚✮✫◗❄●❭❈ ▲ ✄✂ ✾✘❃✧✮✫✪ ✟✞ ▲❡✾ ✡✠ ✫❪ ✾❊❃❍▲✐✮✫✪ ☛✂ ◆❪ ✴P✾☎✶ ●❉❃✑▲✤●❉✦ ✪❇✮✫◗❄●❭❈ ▲ ✄✂ ✑❴ ●❭✪ ✯✫✾❄✪✰✾✲✴ ✮✫❈ ☎✝✆ ✾❥❃✧✮✫✪ ✾ ✡✠ ✵❪❄✾❊❃❍▲❩❪ ✴P✾☎✶ ●❉❃❍▲ ●❝✦✩✪♣✮✫◗❄●♦❈ ●❏▲ ☞✂ ●❏✱ ✾ ✌✠ ❂✮✫❘❥❪✫❈②✾✑❀✍❃❊✦✩❘ ✾❚●♦✪✰✶✫✾❄❪❄✾❄✪ ✌✍ ☎✝✆ ✶✫✾❄✪☎▲q❈ ✎✂ ✦✩❘ ✾❍▲✤●❭❘ ✾✑❀ ✾✲✴P✾❩❤❳✾❛❀❋▲q❫✰✶ ✑✂ ◆❪ ✴P✾☎✶ ●❉❃❍▲ ●❝✦✩✪❇✮✫◗❄●❭❈ ●❏▲ ✄✂ ✑❴ ✮❊❀❋❀✑❫✫❘✇●❭✪✰✯ ●♦✪✰✶✫✾❄❪❄✾❊✶✫✾✲✪✰❃❊✾ Future Samples snow Precipitation rain 0 0.2 0.4 0.6 0.8 1 Temperature Training Sample Test Sample

✆ ❅ ✯ ❱ ✹ ✟ ▲ ▲ ✴ ❅ ✮ ❅ ❀ ▲ ❀ ✆ ✶ ✦ ✞ ✾ ❪ ✂ ✁ ✹ ✂ ❱ ✾❍▲❢▲❋✾❄✴✝✻✇✾❍▲q★✰✦ ✶❄❀ ✱✳✦✵✴t✬ ✾✧✮❂✴③✪❄●❭✪✰✯ ✝✆ ✾❄✴ ●❏■ ❃✧✮☎▲✤●❉✦✩✪ ✮✫✪✰✶ ✮❂✴✷✶❇▲❋✾❊❃✲★✫✪❄● ✡✠ ✩❫✰✾✫❙ ❯✵❱ ☞☛ ● ✌✂ ❄●❉✶✫✾❛❀✤✮✵❘✘❪✫❈②✾✑❀ ●❭✪☎▲❋✦❇▲❍✴ ✮❄●❭✪❚✮✫✪✰✶❇▲ ✾✑❀ ❀❁✾❍▲ ❧♠❱ ●♦✪ ✦✩✪✇▲❍✴ ✮❄●❭✪✘❀ ✾✑▲ s♠❱ ✾✑❀❋▲❡✦✩✪✘▲❋✾ ✾✑▲ ✾✇❃✰✮✫✪ ✦✈◗ ✾❍▲❢▲ ✾✲✴ ★ ☛✂ ✘❀ ▲❍❫✰✶ ✂ ◆❪❂✴✷✾❊✶ ●❉❃❍▲✤●❉✦✩✪✘▲q★✰✾❊✦✵✴ ❯✵❱ ✾❍▲❬▲❋✾✲✴✛❘❞✾✑▲q★✰✦ ✶❄❀ ✱✳✦✵✴✛❈②✾✧✮❂✴③✪❄●❭✪✰✯✭✮✵✪✧✶ ✄✂ ✰✾❄✴ ●❏✱ ●♦✪✰✯ ✴P✾☎✶ ●❉❃❍▲ ✮✫◗❄●❭❈ ●❏▲ ✄✂ ● ☎✂ ❧♠❱ ✮❄●❭✪✎●♦✪❊❀❍●❉✯ ★☎▲ ●❭✪☎▲❋✦✈❈❏✾✰✮ ✴✺✪❄●♦✪✰✯

❅ ✆ ❈ ✦ ✶ ❪ ✞ ✮ ✁ ❅ ❙ ✮ ❅ ✮ ❅ ✟ ✆ ✦ ✆ ✦ ✁ ✂ � ✂ ✟ ❱ ✆ ✁ ✂ ✹ ✂ ✦ ❱ ✂ ✬ ❱ ✶ ❫☎▲❍❈ ●❭✪✰✾ ❯✵❱ ★✰✾ ✮❊❀q●❉❃ ✻❛✦ ✶✫✾✲❈ ❧♠❱ ★✰✾ ✾✑❀❋▲ ✾❍▲✓✹ ✦✩❫✫✪✰✶ s♠❱ ✁� ❃❊❃✧✮✫❘ ❀❛✽❖✮❊①☎✦✵✴t✹ ✦✩❫✫✪✰✶ ▼ ☎✄ ☞❆ ✍ q✹✿✮ ✾✑❀✘✹ ✦✩❫✫✪✰✶ ✮✵❘✘❪✫❈②✾ ❆✿✦✩❘❥❪ ✴P✾✑❀❋❀❍●❝✦✩✪✭✹ ✦✩❫✫✪✰✶ ✦◆✯ ✮❄●♦✪✎●❭✪❊❀q●❉✯✩★☎▲✢●❭✪☎▲❋✦✈❈②✾✧✮ ✴✺✪❄●❭✪✰✯ ❯✵❱ ✁� ✾✲✴✔■ ▲❬▲✤●❭✪✰✯♠❙✼❀✤✮✫❘❥❪✫❈❏✾✘❃☎✦✩❘❥❪✫❈②✾ ✡✠ ❄●❏▲ ✄✂ ✠ ✩❫❂✮✫✪☎▲✤●❏■ ✾✑❀r✦ ✾✲✴✔■ ▲❢▲ ●♦✪✰✯ ❧♠❱ ✾✧✮❂✴③✪❄●❭✪✰✯◆✮✫❈②✯✫✦✵✴✳●❏▲q★✫❘ ✶✫✾ ❀q●❉✯✩✪ ★❂✮☎▲✍●②❀r✮✇✯✫✦ ✴③❫✫✪❄●❭✪✰✯✎❃✲✴✳●❏▲❋✾✲✴✳● ✴P✾ ❈❉✮ ✴P✯✫✾ ❘✓✮❂✴✷✯ ●❭✪❊❀✭✯✫✦ ★❂✮☎▲◆✦✲▲q★✰✾✲✴✇✮✫❈②✯✫✦✵✴ ●❏▲q★✫❘✢❀ ✴P✾ ★ ☛✂ ●❭❣✤✾✲❈ ✂ ✇▲ ●❝✾❄❈❏✶◆✯✫✦ ✶✈✴✷✾ ❀✑❫✫❈ ▲❬❀

❱ ✏ ✂ ✛ ❱ ✍ ✶ ❀ ✮ ❈ ✄ ■ ✁ ✁ ❀ � ❙ ✁ ☛ � ✁ ✻❛✦ ✶✫✾✲❈ ❙✍✹ ✮❊❀q●❉❃ ❀✑❫✫❘❥❪☎▲✤●❉✦✩✪ ✄ t❈ ❀✤✮✫❘❥❪✫❈❏✾ ❀✐✮❂✴✷✾❛✶✩✴ ❤✐✪❇●❭✪✰✶✫✾✲❪ ✾✲✪✰✶✫✾❄✪☎▲q❈ ✂ ❛✱❢✴P✦✩❘ ✦✩❘ ✾❚❫✫✪✫❣❂✪✰✦❊❤✐✪ ●②❀ ▲q✴✳● ◗✫❫☎▲✤●❝✦✩✪ ✑✓✒✕✔✖✞✘✗✚✙ ✒✕✔✖✞✘✗✚✙✢✜✤✣✥✑✦✜ ●②❀❞✮✘❀ ✮✫❘❥❪✫❈❏✾✓❀ ✾✑▲ ✻❛✦ ✶✫✾✲❈ ✾❍■ ✪❄●❏▲✤●❉✦✩✪❊❀ ●♦✪✫❪✫❫☎▲ ❀✑❪❂✮✰❃❊✾ ✁✄✂ ☎✝✆✟✞✡✠☞☛ ✦✩❫☎▲q❪✫❫☎▲❡❀✑❪❂✮✰❃❊✾ ❃✲❈❉✮❊❀❋❀❍● ✾✲✴ ✌✎✍

❜ ✏ ✌ � ✒ ✌ ✂ ✂ ✴ ❅ ✂ ✂ ☛ ✑ ✒ ✌ ✒ ✔ ✂ ✂ ✠ ✕ ✜ ❅ ✖ ❙ ✧ ❙ ☛ ✛ ✶ ✛ ❅ ❱ ✧ ✴ ✦ ❀ � ✒ ✧ ✌ ✁ ✴ ✂ ✂ ✻❛✦ ✶✫✾✲❈ ✾✲✴✳● ☎✂ ✾☎✶ ✠ ✩❫❂✮✫✪☎▲✤●❏▲✤●❉✾✑❀ ★✰✾✓▲❍★❄●♦✪✰✯♣❤❳✾✓❤✝✮✫✪☎▲ ▲❋✦✈❣❂✪✰✦❊❤❞❙ ▲q✴✺❫✰✾✘✾✲✴✺✴✷✦ ✒✕✔ ✗✚✙ ✙ ✎✍ ✌ ✁�✄✂ ☎✝✆ ✞✠✟☛✡✌☞ ★✰✾✓▲❍★❄●♦✪✰✯♣❤❳✾♣★❂✮ ✾✫❙ ✗✚✙ ✒✕✔ ✙ ✎✍ ✙ ✎✍ ✗ ✦✥ ✌ ✒✑✓✂ ☎✝✆ ✞✔✟☛✡✌☞ ✗✙✘✛✚✢✜✤✣ ▲❍✴ ✮❄●❭✪◆✾❄✴③✴P✦✵✴ ✩★ ❁❴ ▲❋✾ ▲❩✾❄✴③✴P✦✵✴ ✩★ ❁❴ ✦✩◗❊❀❁✾✲✴ ✂ ✰✾☎✶ ✾✲✴✺✴P✦✵✴ ✪★ ✤❴ ✶✫✾❄❪❄✾❄✪✰✶ ●♦✪✰✯✂✦✩✪ ❃☎✦✩✪☎▲❋✾ ✌✠ ☎▲ ❨❋✪✰✦✲▲❋✾✫❙✼❤❳✾❚●❉✶✫✾❄✪☎▲✤●❏✱ ✂ ✘▲❍★✰✾✓❀ ✾✑▲ ❤❡●❏▲q★✇▲q★✰✾♣❫✫✪❄●❏✱✳✦✵✴✺❘ ●②❀ ▲❍✴ ●❭◗✫❫☎▲✤●❉✦✩✪ ✦✩✪ ✻❛✦ ✶✫✾✲❈ ✾✲✴✳● ☎✂ ✾☎✶ ✠ ✩❫❂✮✫✪☎▲✤●❏▲✤●❉✾✑❀ ★✰✾✓▲❍★❄●♦✪✰✯♣❤❳✾✓❤✝✮✫✪☎▲ ▲❋✦✈❣❂✪✰✦❊❤❞❙ ✒✕✔ ✗✚✙ ▲q✴✺❫✰✾✘✾✲✴✺✴✷✦ ✙ ✎✍ ✌ ✁�✄✂ ☎✝✆ ✞✠✟☛✡✌☞

✕ ✌ ❱ � ✑ ☞ ✌ ✄ ✏ ✑ ☞ ✂ ☎ � ✆ ✆ ✆ ✌ ✙ ✄ ✂ ❙ � ❱ ✒ � ❙ ✆ ✕ ❨ ☎ ❪ ✏ ✁ ✁ ✄ ✠ Possible Error distributions 0.2 true error Probability 0.1 0 0 0.2 0.4 0.6 0.8 1 Empirical Error Rate ✻❛✦ ✶✫✾✲❈ ❙✍✹✿✮✧❀q●❉❃ ◗❊❀ ✾❄✴ ✂ ✲✮☎▲✤●❉✦✩✪❊❀ ★❂✮☎▲r●②❀❡▲q★✰✾✘✶ ●②❀ ▲q✴✳●❭◗✫❫☎▲✤●❉✦✩✪ ✦✲✱ ✌ ✒✑ ✹❖●❭✪✰✦✩❘✇● ✮✫❈ ✒✡✠ ✎✍ ✜ ✑✏ � ✟✞ ✌ ✌☞ ☎✝✆ � ✂✁ ✕ ✝✆ ☎☛✡ ✴P✦✩◗❂✮✫◗❄●♦❈ ●❏▲ ☞✂ ✦✲✱ ★✰✾✧✮✰✶❄❀ ✾❄✴✺✴✷✦✵✴☛❀✤❜ ●❭✪ ●♦❪❊❀ ✦✲✱r✮✭❃❊✦ ●♦✪ ❤❡●❏▲q★✂◗❄● ✮❊❀ ✌ ✁�